Summation Notation Calculator

Product notation is used less often than summation notation, but you will occasionally see it in your work in computer science. This site is a reference for the factorial n! notation and tries to propose a more complete documentation to this subject. Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits. We give a few examples. Typical notation to designate a vector is a boldfaced character, a character with and arrow on it, or a character with a line under it (i. Series and Sigma Notation 2 - Cool Math has free online cool math lessons, cool math games and fun math activities. Mathematica is Wolfram's original, flagship product—primarily aimed at technical computing for R&D and education. Lesson 16 Parts of Natural Numbers 2. Guidelines to use the calculator If you select a n, n is the nth term of the sequence If you select S n, n is the first n term of the sequence For more information on how to find the common difference or sum, see this lesson arithmetic sequence. In some cases we need to find an equivalent representation of a given summation, but that has different summation limits. Byju's Adding Scientific Notation Calculator is a tool which makes calculations very simple and interesting. This can leave up to 3 digits to the left of the decimal place and may require the addition of either one or two trailing zeros. Also useful in converting numbers to scientific notation is the exponent calculator. Many summation expressions involve just a single summation operator. Learn more about the use of binary, or explore hundreds of other calculators addressing math, finance, health, and fitness, and more. EXAMPLES USING MATHCAD 14 Basic Operations: 22+ =4 Type the = sign to get a result. in memory or on disk) by an algorithm. Write the following sums. Shorthand notation for Maxterm. 4 Asymptotic Approximations of Finite Sums Frequently, we are able to express a quantity as a finite sum, and therefore we need to be able to accurately estimate the value of the sum. Let f be a function whose domain includes the integers from n through m. Calculator for the multiplication with the product symbol Pi, Π. linear dependence, orthogonal complement, visualisation, products This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games. 3 represents a Venn diagram showing two sets A and B, in the general case where nothing is known about any relationships between the sets. 4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. here c is any number. Instead of notation, we use notation, where the n is the input variable, called the index, and n is the output result. The only calculator series I'm familiar with is the Casio fx series, so I'll give an answer based on them. Although it can appear scary if you've never seen it before, it's actually not very difficult. • m is the lower limit and • n is the upper limit of the summation. A vector quantity has magnitude and direction. Notice that we’ve switched x and y from the paragraph above! Differentiating the exponential function x = e y in this switched notation, d x d y = e y = x, so d y d x = 1 x. It is capable of computing sums over finite, infinite (inf) and parametrized sequencies (n). Note that index i can be replaced by any other index and the results will be the same. Select Sum Function: Press F3 (for Calc menu) Press 4 (for. Suppose we're working with 8 bit quantities (for simplicity's sake) and suppose we want to find how -28 would be expressed in two's complement notation. In other words, we are to repeatedly add ka k, which we call the argument of the sum, or the summand, starting with k = 1 and ending with k = 4. Summation of the terms of a sequence: The variable j is referred to as the index of summation. Polar - Polar. Let's see how to express a summation of numbers in mathematics using sigma notation. EXAMPLES USING MATHCAD 14 Basic Operations: 22+ =4 Type the = sign to get a result. With three or more assets, the investment oppor-. 45 x 10^5 or 3. #mathematics #ti84 #maths ***** Don’t forget guys, if you like this. The vectors we will be adding are. Problems: Significant Figures State the number of significant figures in each of the following measurements. A boolean expression consisting entirely either of minterm or maxterm is called canonical expression. When an algorithm contains an iterative control construct such as a while or for loop, its running time can be expressed as the sum of the times spent on each execution of the body of the loop. Sums of numbers, such as the one above, are often called series. This notation may look strange at first, and clearly if the numbers were entered as shown you would get the number three-hundred and twenty-one! To make this work you need an extra key that tells the calculator when you have finished entering each number. 5 we learn to work with summation notation and formulas. Notation for sequences and sets including indexing, summation, and set membership. Calculating the approximate area with summation notation requires formulas, and these calculus instructions help. Upload failed. Find more Mathematics widgets in Wolfram|Alpha. Finding a Sum 1) Go to the Greek keyboard next to the a-z button. To enter a number in scientific notation use a carat ^ to indicate the powers of 10. In Notes x4. Why? Because there are no methods (covered in the ISM) to compute an infinite sum otherwise. Summation notation is particularly useful if you want to sum over elements of a set. Or read the Calculator Tutorial to learn more. Only this variable may occur in the product term. This calculator for to calculating the sum of a series is taken from Wolfram Alpha LLC. Calculator Use. Sometimes our sum has a pattern which enables us to write the sum usnig sigma notation. Summation value of the given function is displayed in a fraction of seconds. Here's a simple example. the summation notation is a lot like a for loop. 66 x 10 5 ; 0. here c is any number. Slightly more general, an expression of the form is called a power series with center. 5 Techniques you can use to get help if you are struggling with mathematical notation. Click HERE to return to the list of problems. It indicates that the terms of this summation involve factorials. Start Value. The earliest known detailed discussion of binomial coefficients is in a tenth-century commentary, by Halayudha, on an ancient Sanskrit text, Pingala's Chandaḥśāstra. The Greek capital letter, ∑ , is used to represent the sum. Sum of the n members of arithmetic progression is Below is the calculator of nth term and sum of n members of progression. factorial of a number calculator - formula, step by step calculation & solved example problems online to calculate the factorial of a given number (positive integer) n. Lesson 13 Dividing Decimals. How to calculate Summation / Sigma - Definition, Formula and Example Definition Summation is the process of adding a set of numbers, and it is denoted by the symbol ∑. The product is a repeated multiplication with a start value m and an end value n. here c is any number. The series 4 + 8 + 12 + 16 + 20 + 24 can be expressed as ∑ n = 1 6 4 n. Free series convergence calculator - test infinite series for convergence step-by-step. " Therefore, if the sigma is followed by the letter X, it means that you should add up all of the X scores. You can operate the online calculator directly from your computer's numerical keyboard, as well as using the mouse. Question: Use The Summation Formulas To Rewrite The Expression Without The Summation Notation. In Notes x4. • m is the lower limit and • n is the upper limit of the summation. As far as I'm aware, Casio fx- 991ES and any calculator beyond that can perform summations using sigma notation. Summation Notation Involves: The summation sign, S, instructs us to sum the elements of a sequence. Canonical Expression. Show Instructions In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`. Following are the steps to get the shorthand notation for maxterm. A vector is a number with direction. A typical sum written in sigma notation looks like this: 4 k 0 (k2 3) The symbol "Σ" is the Greek capital letter sigma, which stands for "sum". The Octal Calculator is used to perform addition, subtraction, multiplication and division on two octal numbers. Byju's Adding Scientific Notation Calculator is a tool which makes calculations very simple and interesting. Sigma notation calculator is an effective tool which gives the short form of a detailed sum. Many statistical formulas involve adding a series of numbers. The calculator is now in scientific notation mode. How to Use the Summation Calculator? The procedure to use the summation calculator is as follows:. Use the Shortest Unit Fraction Sum Calculator or the Fixed Length Egyptian Fractions Calculator to find all the Egyptian Fractions but this calculator is quicker if you just want one. This is probably the easiest way to learn the basic operation of Maxima. Σ (sigma) indicates sum and lower case “m” indicates minterms. Practise maths online with unlimited questions in more than 200 year 11 maths skills. Sum and Product Notation: Delimited Forms The capital Greek letter Σ (sigma) denotes summation. linear dependence, orthogonal complement, visualisation, products This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games. Index notation provides a very powerful tool for proving many identities in vector calculus, or for manipulating formulae for multi-dimensional calculus. It is also called sigma notation because the symbol used is the letter sigma of the Greek alphabet. 2 Calculations Involving Powers of Ten When multiplying powers of ten, the exponent for the product is the sum of the exponents in all of the factors. In the cases where series cannot be reduced to a closed form expression an approximate answer could be obtained using definite integral calculator. We are drawing three cards for the flop, so C(50,3) = 19,600 possible flop combinations. num_range sum (num_range) Adding like a mathematician. Anyone here have a TI-83 or TI-84 graphing calculator? I'm trying to find a way to do "Sigma Notation" sums. Masingale, Le Moyne College Department of Chemistry. Calculate enormous mathematical equations from within your browser. The sum expressed in sigma notation would then be: In order to evaluate the summation, we must understand. Sigma notation is most useful when the “term number” can be used in some way to calculate each term. Related Math Calculators. High-quality display of mathematics notation in all browsers. For 2 number x1 and x2: x 1 = a 1 × 10 b1. And the main point of this lecture is either remind you or tell you about these concepts for the first time and to tie them back in to sigma notation. Logarithm rounds by the input's number of significant figures as the result's number of decimals. Calculator Use. Press 2nd quit. , same units) can be combined by basic vector operations. closed as unclear what you're asking by user147263, Harish Chandra Rajpoot, Daniel, user99914, Tim Raczkowski Dec 1 '15 at 3:14. Free series convergence calculator - test infinite series for convergence step-by-step. Description. The variable age of a student can be denoted by x. De-vore (fifth edition), published by Wadsworth. In order to illustrate why this is true, think about the inflating sphere again. Enter a number or a decimal number or scientific notation and the calculator converts to scientific notation, e notation and engineering notation formats. As running variable, which is increased by 1 in each step, i is used. Show Instructions In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`. Statistical Sums 3 Doing Sums on the Calculator - Duration: 10:46. It is capable of computing sums over finite, infinite (inf) and parametrized sequencies (n). 1's Complement Arithmetic The Formula N = (2 n −1)− N where: n is the number of bits per word N is a positive integer N is -N in 1's complement notation For example with an 8-bit word and N = 6, we have: N = (28 −1)−6 = 255 − 6 = 249 =11111001 2 In Binary An alternate way to find the 1's complement is to simply. Product notation for a series of numbers such as 2 × 4 × 6 × 8 × 10 × 12 × 14 × 16 × 18 × 20 (the product of the first ten even numbers) is denoted using the uppercase Greek letter pi (∏). B-Summation Notation. Click HERE to return to the list of problems. To enter a number in scientific notation use a carat ^ to indicate the powers of 10. Press Enter to save your selection. Hence, AA−1 = A−1A = I A matrix must be square to have an inverse, but not all square matrices have an inverse. When an algorithm contains an iterative control construct such as a while or for loop, its running time can be expressed as the sum of the times spent on each execution of the body of the loop. Sigma Notation of a Series A series can be represented in a compact form, called summation or sigma notation. Statistical Sums 3 Doing Sums on the Calculator - Duration: 10:46. For example, a number such as 2000 would be written as 2 x 103 if it contains one significant figure, and as 2. Start Value. If you do not specify k, symsum uses the variable determined by symvar as the summation index. Summation notation is used to denote the sum of values. In this section we give a quick review of summation notation. The product is a repeated multiplication with a start value m and an end value n. Summation notation is analogous to sequence notation \(\{a_n\}\) with the exception that in sequence notation the sequence usually starts with \(n=1\) and procedes indefinitely, so it is unnecessary to specify that \(n\) goes from \(1\) to infinity. If you want the limits of an integral/sum/product to be specified above and below the symbol in inline math mode, use the \limits command before limits specification. Click here to jump to the vector addition calculator at the bottom of this page. And that's where Sigma notation comes from. HP adjusted the postfix notation for a calculator keyboard, added a stack to hold the operands and functions to reorder the stack. jn14955f 2,739 views. Sum of the Powers of the Integers. Polar - Polar. com and learn study guide, scientific and a large number of other algebra subjects. Sigma Notation Rules Made Easy with 9 Examples!. The NRICH Project aims to enrich the mathematical experiences of all learners. However, care must be taken to ensure that you are calculating the mean for a population (the whole group) and not a sample (part of the group). Finding a Sum 1) Go to the Greek keyboard next to the a-z button. Write out the mathematical steps you took to calculate the mean. Graphs of functions are graphs of equations that have been solved for y! The graph of f(x) in this example is the graph of y = x 2 - 3. You can also enter numbers in e notation. 2 Summation notation Summation notation. Given two number sets A and B, this determines the following: * Union of A and B, denoted A U B * Intersection of A and B, denoted A ∩ B * Elements in A not in B, denoted A - B. Scientific Notation All numbers, regardless of magnitude, can be expressed in the form: N x 10 n where N is a number, either an integer or decimal, between 1 and 10. You cannot do calculations like "Give me the sum of all integers from 1 to 100" with the TI-30XA, you'd need a far more sophisticated calculator. Notation To calculate in scientific notation, use the x10π button as well as make sure your calculator is in Scientific notation in the mode menu. Although any one of such factored forms may be more useful than the original form of the number, a special name is given to the last form. The Java Tutorials have been written for JDK 8. number1 to number30 are up to 30 numbers or ranges/arrays of numbers whose sum is to be calculated. Start studying Summation Notation. Calc commands use the digits, letters, and punctuation keys. Then, find the sum of the squares of the deviationscan you see why we squared them before adding the values? Divide the sum of the squares of the deviations by n-1. The Summation Calculator is a free online tool that displays the sum of the given series. Explore math with desmos. Summation notation provides for us a compact way to represent the addends in sums such as these. If we needed more than 3 signficant figures, we pulled out our lengthy logarithm tables. Math Help Boards: Sum Calculator. An infinite geometric series has an infinite number of terms. Use n = 50 equal subdivisions. Also for: Fx-83gt plus. Sums can also be infinite, provided that the terms eventually get close enough to zero–this is an important topic in calculus. Area Under a Curve by Limit of Sums Riemann Sum Tables First. Python HOWTOs in-depth documents on specific topics. The Sigma symbol, , is a capital letter in the Greek alphabet. After many searches I couldn't find a single page containing summation formulas for polynomials of order greater than 4. For example, to enter the number 3. Statistics Notation. Calculate the Product. Most Commonly. We will also introduce a brief overview of sequences, material not included in the text. If there was a carry out, the extra bit is shown on the next line. Summation notation works according to the following rules. Summation notation is used to define the definite integral of a continuous function of one variable on a closed interval. Summation notation provides for us a compact way to represent the addends in sums such as these. The variable of summation, i. Recall that when we use big-O notation, we drop constants and low-order terms. So mathematicians said, well, let's find some notation, instead of having to do this dot dot dot thing-- which you will see sometimes done-- so that we can more cleanly express these types of sums. Only in the base 10 (decimal) system can words such "hundred", "thousand", "million" and so on, be used. We're going to finish up our video series on summation and use of the summation symbol, and we're going to remind you what mean and variance are. We define We call i the index of summation, n is the lower limit of summation, and m is the upper limit of summation. There are 602,000,000,000,000,000,000,000 molecules in 18 grams of water. Then simplify. If a sum cannot be carried out explicitly by adding up a finite number of terms, Sum will attempt to find a symbolic result. Taylor’s Formula (The Extended Mean Value Theorem) October 19, 2000 §1 When f is a function and k ≥0 is an integer the notation f(k) denotes kth derivative of f. Sigma notation is a great shortened way to add a series of numbers, but it can be intimidating if you don't understand how to read it. Hauskrecht Summations Example: • 1) Sum the first 7 terms of {n2} where n=1,2,3,. Sigma (Summation) Notation. Scientific notation converter Scientific notation calculations. Enter Fraction #2 into the second box. Summations for Power Series It is sometimes difficult to express a power series in summation notation. a) 230 cm ans. What this really means, is that you're going to assign a "term number" to each term, ie the first term, the second term, the third term, etc. Products of Sci. 12 x 10-3 (to the power of m. The variable. A number expressed as the product of a number between 1 and 10 (including 1) and a power of 10 is said to be in scientific form or scientific notation. This summation notation calculator can sum up many types of sequencies including the well known arithmetic and geometric sequencies, so it can help you to find the terms including the nth term as well as the sum of the first n terms of virtualy any series. Summation Notation: Given a sequence fa ng 1 n=k and. Split the summation into smaller summations that fit the summation rules. Input LaTeX, Tex, AMSmath or ASCIIMath notation (Click icon to switch to ASCIIMath mode) to make formula. The calculator also has plenty of memory slots. , upper-case) letters are different from lowercase letters. In any question where one must find the sum of a series given in the form where each term is positive, we must first convert the sum to sigma notation. The Sigma symbol, , is a capital letter in the Greek alphabet. If , the series does not converge (it is a divergent series). You can also enter numbers in e notation. Sigma notation calculator is an effective tool which gives the short form of a detailed sum. SUM ignores any text or empty cell within a range or array. Thus, we record a zero for the. Use the Shortest Unit Fraction Sum Calculator or the Fixed Length Egyptian Fractions Calculator to find all the Egyptian Fractions but this calculator is quicker if you just want one. In some cases we need to find an equivalent representation of a given summation, but that has different summation limits. The Octal Calculator is used to perform addition, subtraction, multiplication and division on two octal numbers. In this lesson, we'll be learning how to read Greek letters. Fortunately there is a convenient notation for expressing summation. This calculator is concerned only with changing numbers into different bases and no attempt is made to explain what these numbers are and how they work. Anyone here have a TI-83 or TI-84 graphing calculator? I'm trying to find a way to do "Sigma Notation" sums. Table 2 shows the use of this notation. Practice worksheets for converting numbers from standard numeric notation into written (word form) notation. The study of probability mostly deals with combining different events and studying these events alongside each other. Let's first briefly define summation notation. The delimited form Xn k=1 ak = a1 +a2 +a3 +···+an. If an input is given then it can easily show the result for the given number. Engineering notation has an exponent which is a multiple of 3. cpp, that calculates the summation of a function, e. Be careful to distinguish between this variable and the index for the sum! We can also use P notation when we have variables in our terms. Listing of the mathematical notations used in the Mathematical Functions Website. Example 1: Find. And that's where Sigma notation comes from. Free Algebra Solver and Algebra Calculator showing step by step solutions. In this lesson, we'll be learning how to read Greek letters. Interpretation of the mean. Students, teachers, parents, and everyone can find solutions to their math problems instantly. SUM(), SERIESSUM() are not suitable in this case. 1 Sigma notation One strategy for calculating the area of a region is to cut the region into simple shapes, calculate the area of each simple shape, and then add these smaller areas together to get the area of the whole region. How to Use Summation Formulas in Microsoft Excel. 4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Or read the Calculator Tutorial to learn more. End Value. One is by using summation notation and one is by using subscript notation similar to how we write explicit forms of sequences. It is possible that at a later date I will add some problems to this section but doing that is very low on my list of things to do. Scientific notations addition. Clear and Free! Simple Calculator - A nice Simple Free Online Calculator. The sum notation uses the capital Greek letter sigma as follows: Thus if x 1 = 6, x 2 = 7 and x 3 = -2, then. Summation formulas. the variable which is being summed; The variable of summation is represented by an index which is placed beneath. We begin with a de nition, which, while intimidating, is meant to make our lives easier. Calculator Bitcoin. Now that all of the basic rules of scientific notation and its applications have been outlined, we can learn how the scientific calculator can help us with scientific notation conversions: Using A Graphing Calculator To Express Scientific Notation Edit. This vector addition calculator can add up to 10 vectors at once. Turns the calculator on or clears the data. Mathematica is Wolfram's original, flagship product—primarily aimed at technical computing for R&D and education. important- excel sigma notation does anyone know how to do Capital-sigma notation on excel with steps ∑((x-n)*Y^n) from n = 1 , to n = x i. As running variable, which is increased by 1 in each step, i is used. Index notation provides a very powerful tool for proving many identities in vector calculus, or for manipulating formulae for multi-dimensional calculus. Write out the mathematical steps you took to calculate the mean. If you were asked to add all of the items up in summation notation, you would see: Σ(x) which equals 1 + 2 + 5 + 7 + 9 = 24. Click on the link with each question to go straight to the relevant page. You can operate the online calculator directly from your computer's numerical keyboard, as well as using the mouse. Scientific Notation - Sample Math Practice Problems The math problems below can be generated by MathScore. Sigma notation is a great shortened way to add a series of numbers, but it can be intimidating if you don't understand how to read it. Start studying Summation Notation. In the cases where series cannot be reduced to a closed form expression an approximate answer could be obtained using definite integral calculator. F = symsum(f,k,a,b) returns the sum of the series f with respect to the summation index k from the lower bound a to the upper bound b. The sum is evaluated until n = 10 which is written on top of the sum. The summation symbol can distribute over subtraction. Given two number sets A and B, this determines the following: * Union of A and B, denoted A U B * Intersection of A and B, denoted A ∩ B * Elements in A not in B, denoted A - B. Let's review the basic summation rules and sigma notation to find the limit of a sum as n approaches infinity. The definition of the summation process: Summation is the addition of a set of numbers. Graphs of functions are graphs of equations that have been solved for y! The graph of f(x) in this example is the graph of y = x 2 - 3. Summation value of the given function is displayed in a fraction of seconds. CHAPTER 3: SUMMATIONS. To solve typical arithmetic sequences problems you can use this calculator. Write the sigma notation. To add a finite sequence of values, rather than compute a formula, use the add command. A scientific calculator executes all standard operations plus sin, cos, tan, logarithms, factorials, n-th roots. Number Of Subsets (Powersets) Calculation A set is called the power set of any set, if it contains all subsets of that set. Sigma Notation of a Series A series can be represented in a compact form, called summation or sigma notation. Summation definition is - the act or process of forming a sum : addition. 5 Techniques you can use to get help if you are struggling with mathematical notation. Displacement, velocity, momentum, force, and acceleration are all vector quantities. For example, if , then. please don't hesitate to share with us your ideas!. SUM ignores any text or empty cell within a range or array. Calculate a Double Sum. Select Scientific. Notice that summation notation is just a notation. On the TI 83, 84 Calculator: 2nd - STAT (list)-MATH-#5 for Sum 2nd - STAT(list)-OPS-#5 for Seq. 4 APPENDIX A SCIENTIFIC NOTATION AND POWERS OF TEN CALCULATIONS A. The summation symbol can distribute over addition. 66 x 10 5 ; 0. Table of Content. Sometimes our sum has a pattern which enables us to write the sum usnig sigma notation. i k hM 6a6d peM swnintrhD 5ITn 5fQiknIi ct 5eC YA3l 9g 6eNbaraw 62 L. For example, adding up the sum of 1/n does not converge, whereas the sum of 1/n² converges to π²/6, a rather unexpected result. Calculus Of One Real Variable - By Pheng Kim Ving Chapter 9: The Integral - Section 9. A typical element of the sequence which is being summed appears to the right of the summation sign. A vector quantity has magnitude and direction. Then simplify. Although any one of such factored forms may be more useful than the original form of the number, a special name is given to the last form. Many statistical formulas involve adding a series of numbers. asin inverse sine (arcsine) of a value or expression acos inverse cosine (arccos) of a value or expression atan inverse tangent. 5*k/36)) k=1 Basically, I need to find a sum of square-roots where in each individual squareroot the k-value will be substituted by an integer from 1 to 14. Use summation notation to express the sum of all numbers; Use summation notation to express the sum of a subset of numbers; Use summation notation to express the sum of squares; Many statistical formulas involve summing numbers. The summation operator governs everything to its right. The notation on the left side denotes the definite integral of f(x) from a to b. Roughly speaking, this integral is the limiting case of the formula for the expected value of a discrete random variable Here, is replaced by (the infinitesimal probability of ) and the integral sign replaces the summation sign. The calculator above computes population standard deviation and sample standard deviation, as well as confidence interval approximations. The rounding calculator is a great tool to use to accomplish this task. Summation notation is used to define the definite integral of a continuous function of one variable on a closed interval. jn14955f 2,739 views. " For example, let's say you had 5 items in a data set: 1,2,5,7,9; you can think of these as x-values. Why Did/Does HP Use RPN?. All operations we execute are visible on the panel above the buttons. Taylor’s Formula (The Extended Mean Value Theorem) October 19, 2000 §1 When f is a function and k ≥0 is an integer the notation f(k) denotes kth derivative of f. nth Term Calculator is a maths activity ideal for use with an interactive whiteboard. A vector is a number with direction. A convenient notation for the sum of the terms of the sequence uses the sigma notation since it uses the Greek letter sigma, written as ∑. F = symsum(f,k,a,b) returns the sum of the series f with respect to the summation index k from the lower bound a to the upper bound b. Use 1 as the lower limits of summation and i for the index of summation. Most Calculator commands deal explicitly with the stack only, but there is a set of commands that allow you to search back through the trail and retrieve any previous result. This summation notation calculator can sum up many types of sequencies including the well known arithmetic and geometric sequencies, so it can help you to find the terms including the nth term as well as the sum of the first n terms of virtualy any series.