Science:Infinite Series Module/Units/Unit 1/1.2 Sigma Notation/1.2.02 Sigma Notation Terminology

Terminology

The infinite sum

$a_{1}+a_{2}+a_{3}+\ldots$

can be written in a more compact way. Using the capital greek letter sigma, $\Sigma$, we may write this sum as

$a_{1}+a_{2}+a_{3}+\ldots =\sum _{k=1}^{\infty }a_{k}$

We often use the following terminology when using this notation

• the general term of the sum is $a_{k}$
• the index of summation is $k$
• the limits of summation are 1 and $\infty$, although in general the limits can be any integer, $-\infty$, or $+\infty$.

Simple Example

Consider the infinite series

${\frac {1}{2+3^{2}}}+{\frac {2}{2+4^{2}}}+{\frac {3}{2+5^{2}}}+\ldots =\sum _{k=3}^{\infty }{\frac {k-2}{2+k^{2}}}$

In this example, the general term is

${\frac {k-2}{2+k^{2}}},$

the index of summation is $k$, and the limits of summation are 3 and infinity.