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

Terminology

The infinite sum

$a_1+a_2+a_3+\dots$

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

$a_1+a_2+a_3+\dots =\sum _{k=1}^{\mathrm{\infty }}{a}_k$

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 $\mathrm{\infty }$, although in general the limits can be any integer, $-\mathrm{\infty }$, or $+\mathrm{\infty }$.

Simple Example

Consider the infinite series

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

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.