# Thread: power series for 1/(1-x)^2

1. ## power series for 1/(1-x)^2

so.. i know that the power series is $\sum_{n=0}^\infty \ nx^{n-1}
$
or $\sum_{n=0}^\infty \ (n+1)x^n$

what i'm not sure about is.. how to find the radius of convergence and the interval of convergence

my book says that the radius of convergence is 1, but beyond that, i don't know how or why

please help?

2. Originally Posted by buttonbear
so.. i know that the power series is $\sum_{n=0}^\infty \ nx^{n-1}
$
or $\sum_{n=0}^\infty \ (n+1)x^n$

what i'm not sure about is.. how to find the radius of convergence and the interval of convergence

my book says that the radius of convergence is 1, but beyond that, i don't know how or why

please help?
use the ratio test to find the interval of convergence ...

$\lim_{n \to \infty} \left|\frac{(n+2)x^{n+1}}{(n+1)x^n}\right| < 1$

$|x| \lim_{n \to \infty} \frac{n+2}{n+1} < 1$

$|x| \cdot 1 < 1$

$-1 < x < 1$