summation

(noun)

A series of items to be summed or added.

Related Terms

  • sigma
  • arithmetic sequence
  • vector

Examples of summation in the following topics:

  • Series and Sigma Notation

    • Summation is the operation of adding a sequence of numbers, resulting in a sum or total.
    • For finite sequences of such elements, summation always produces a well-defined sum.
    • One way to compactly represent a series is with sigma notation, or summation notation, which looks like this:
    • In this formula, i represents the index of summation, xix_ix​i​​ is an indexed variable representing each successive term in the series, mmm is the lower bound of summation, and nnn is the upper bound of summation.
    • The "i=mi = mi=m" under the summation symbol means that the index iii starts out equal to mmm.
  • Sums and Series

    • The summation of all the terms of a sequence is called a series, and many formulae are available for easily calculating large series.
    • Summation is the operation of adding a sequence of numbers; the result is their sum or total.
    • If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation.
    • where iii represents the index of summation; xix_ix​i​​ is an indexed variable representing each successive term in the series; mmm is the lower bound of summation, and nnn is the upper bound of summation.
    • The "i=mi=mi=m" under the summation symbol means that the index iii starts out equal to mmm.
  • Applications and Problem-Solving

    • Using equations for arithmetic sequence summation can greatly facilitate the speed of problem solving.
    • To apply this to the first summation of all the even numbers between 50 and 100, we would want to add until the 50th term:
  • Summing Terms in an Arithmetic Sequence

  • Binomial Expansion and Factorial Notation

    • In order to solve this, we will need to expand the summation for all values of kkk.
  • Binomial Expansions and Pascal's Triangle

    • Using summation notation, it can be written as:
  • Partial Fractions

    • The denominators of the terms of this summation, gj(x)g_{j}(x)g​j​​(x), are polynomials that are factors of g(x)g(x)g(x), and in general are of lower degree.
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