# Homework Help: Power Series help.

1. Apr 3, 2014

### STJ

1. The problem statement, all variables and given/known data
Find interval of convergence and radius of convergence of the following infinite series.

Series from n=1 to infinity ((-3)^n * x^n) / (n*(n)^1/2)

2. Relevant equations
Ratio test

3. The attempt at a solution

I've started with the ratio test and end up getting 3xn^(3/2) / (n+1)^(3/2) after cancellation. I don't know how to cancel anything else out, I'm guessing L'Hopital's rule but that doesn't seem right. I feel like I should be able to do more cancellation here.

2. Apr 3, 2014

### Ray Vickson

Just use elementary algebra:
$$\frac{n^{3/2}}{(n+1)^{3/2}} = \left( \frac{n}{n+1}\right)^{3/2}$$
What happens to this ratio when $n \to \infty?$

3. Apr 3, 2014

### PeroK

What can you say about n/(n+1) as n →∞?

4. Apr 3, 2014

### STJ

I swear I think to hard sometimes. Thanks.

And as n/(n+1) n →∞ = 1

R=1/3, Interval of convergence will be [-1/3, 1/3]

5. Apr 3, 2014

### PeroK

Are you sure it converges for x = -1/3?