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Series

A series is the indicated sum of the terms of a sequence.

A series can be written in an abbreviated form by using the Greek letter $\sum$(sigma), called the summation sign.  For instance, to abbreviate the writing of the series $2+4+6+8+\cdots +50$ first notice that the general term of the series is $2n$.  The series begins with the term for $n=1$ and ends with the term for $n=25$.  Using sigma notation, you can write this series as ${\displaystyle \sum _{n=1}^{25}2n}$, which is read “the sum of $2n$ for values of $n$ from $1$ to $25$.”

$\begin{array}{l}{\displaystyle \sum _{n=1}^{25}2n}=2\cdot 1+2\cdot 2+2\cdot 3+2\cdot 4+\cdots +2\cdot 25\\ =2+4+6+8+\cdots +50\end{array}$

There are formulas to help you quickly find the value of finite arithmetic series, finite geometric series, and certain kinds of infinite geometric series.