# How do you find the sum of the infinite geometric series 6+5+(25/6)+....?

Jan 3, 2016

$S u m = 36$

#### Explanation:

${a}_{2} / {a}_{1} = \frac{5}{6}$
${a}_{3} / {a}_{2} = \frac{\frac{25}{6}}{5} = \frac{5}{6}$
$\implies r = \frac{5}{6}$ and ${a}_{1} = 6$

Sum of infinite geometric series is given by
$S u m = S = {a}_{1} / \left(1 - r\right) = \frac{6}{1 - \frac{5}{6}} = \frac{36}{6 - 5} = \frac{36}{1} = 36$
$\implies S u m = 36$