# Math Help - When is this power series convergent?

1. ## When is this power series convergent?

For which $x \in R$ is it convergent?

$\sum\limits_{n=0}^\infty(-1)^n \frac{(x-2)^n}{5n9^n}$

Thank you!

2. $\displaystyle\sqrt[n]{{\frac{{\left| {x - 2} \right|^n }}{{5n9^n }}}} \to ?<1$

3. First, find the radius of convergence...

$R=\mid\frac{a_n}{a_{n+1}}\mid$

Then...

$-R

Check:

$x=R, x=-R$