Infinite Series Formula

Infinite series is one of the important concept in mathematics. It tells about the sum of series of numbers which do not have limits.

The sum of an infinite series can be denoted as $\sum_{0}^{\infty}r^{n}$. The formula for infinite series is given by,

\[\large \sum_{0}^{\infty}r^{n}=\frac{1}{1-r}\]

Solved Examples

Question 1: Evaluate $\sum_{0}^{\infty }(\frac{1}{2})^{n}$?


The sum of given series is,
$\sum_{0}^{\infty }(\frac{1}{2})^{n}$

So the series can be written as,

$\sum_{0}^{\infty }(\frac{1}{2})^{n}$ = $(\frac{1}{2})^{0}$+$(\frac{1}{2})^{1}$+$(\frac{1}{2})^{2}$+$(\frac{1}{2})^{3}$+…………..

Here common ratio, r is $\frac{1}{2}$
Infinite series formula is,

$\sum_{0}^{\infty }r^{n}$ = $\frac{1}{1-r}$

So, $\sum_{0}^{\infty }r^{n}$ = $\frac{1}{1-\frac{1}{2}}$ = 2


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