Examples of summation in the following topics:
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- 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, $x_i$ is an indexed variable representing each successive term in the series, $m$ is the lower bound of summation, and $n$ is the upper bound of summation.
- The "$i = m$" under the summation symbol means that the index $i$ starts out equal to $m$.
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- 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 $i$ represents the index of summation; $x_i$ is an indexed variable representing each successive term in the series; $m$ is the lower bound of summation, and $n$ is the upper bound of summation.
- The "$i=m$" under the summation symbol means that the index $i$ starts out equal to $m$.
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- 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:
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- In order to solve this, we will need to expand the summation for all values of $k$.
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- Using summation notation, it can be written as:
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- The denominators of the terms of this summation, $g_{j}(x)$, are polynomials that are factors of $g(x)$, and in general are of lower degree.