# How do you find the sum of the infinite geometric series 4 + 3 + 9/4 + ...?

Mar 18, 2018

Sum of the infinite geometric series is $16$.

#### Explanation:

In this geometric series, firt term is $4$ and common ratio is $\frac{3}{4}$ as ratio between a term and its immediating preceding term is $\frac{3}{4}$.

As common ratio is less than $1$, the sum of infinite series would be $\frac{a}{1 - r}$, where $a$ is first term and commonb ratio is $r$.

Hence the sum of the infinite geometric series $4 + 3 + \frac{9}{4} + \ldots$ is

$\frac{4}{1 - \frac{3}{4}} = \frac{4}{\frac{1}{4}} = 4 \times \frac{4}{1} = 16$