# How do you find the sum of the infinite geometric series 1.1(0.5)^(n - 1)?

May 6, 2016

Sum of the infinite geometric series is $2.2$

#### Explanation:

This is a geometric series whose first term $a$ is $1.1$

and ratio $r$ of a term to its preceding term is $0.5$

As $r < 1$, the series is convergent and sum is

$\frac{a}{1 - r} = \frac{1.1}{1 - 0.5} = \frac{1.1}{0.5} = 1.1 \times 2 = 2.2$