# Thread:

1. ## Power Series

I need help for the following problem.

Find the radius of convergence for the power series:

$\sum_{j=1}^{\infty} (x/2)^j$

2. Originally Posted by larson
I need help for the following problem.

Find the radius of convergence for the power series:

$\sum_{j=1}^{\infty} (x/2)^j$
By the root test, the series converges for all $x$ such that $\lim_{j \to \infty} |(x/2)^j|^{1/j} < 1$

don't forget to check the end points

3. Originally Posted by Jhevon
By the root test, the series converges for all $x$ such that $\lim_{j \to \infty} |(x/2)^j|^{1/j} < 1$

don't forget to check the end points
how do i know what my endpoints are?

4. Hello,

Find the radius of convergence R, then look at the convergence/divergence of the series if x=R and x=-R
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