# How do you find the sum of the infinite geometric series a1=26 and r=1/2?

Dec 29, 2015

$52$

#### Explanation:

Sum of infinite geometric series is given by
$S = {a}_{1} / \left(1 - r\right)$
Where $S$ is the sum of the series ${a}_{1}$ is the first term and $r$ is the common ration.
$\implies S = \frac{26}{1 - \frac{1}{2}} = \frac{52}{2 - 1} = \frac{52}{1} = 52$
$\implies S = 52$ Hence the sum of the given infinite geometric series is $52$.