# How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given 1-1/3+1/9-...+(-1/3)^n+...?

Feb 19, 2017

$0.75$

#### Explanation:

The Maclaurin series

$\frac{1}{1 + x} = 1 - x + {x}^{2} - {x}^{3} + \ldots$ is valid for $- 1 < x < 1$.

Here, x = 1/3.

So, the given series converges to $\frac{1}{1 + \frac{1}{3}} = 0.75$.