# Homework Help: Power Series

1. Nov 11, 2014

### Grunting7

1. The problem statement, all variables and given/known data

n=3 ∑ ((-1)n (x+3)3n)/(2nlnn)

Find radius of convergence, interval of convergence, values for x which series is: absolutely convergent, conditionally converge or divergence.

2. Relevant equations

3. The attempt at a solution
I applied the Ratio Test and got

|(x+3)3| lim n--> ∞ (-1(lnn))/(ln(n+1))

Then I used l'Hospitals to get the limit and got -1/2.
So then it's -1/2 * |(x+3)3| = L. Then do the radius and interval stuff.

The problem is that it's -1/2 and the radius can't be negative. I've had one or two similar problems where I keep getting a negative radius. Not sure what I am missing.

2. Nov 11, 2014

### Panphobia

The absolute value of -1 is 1. When you're pulling out the (x+3)^3, you have to keep the absolute value on the lnn/ln(n+1) or pull out the -1 with the (x+3)^3. Also I am pretty sure you're missing (1/2) somewhere in your limit.

3. Nov 11, 2014

### Grunting7

Wow, did not even know that. Solves the negative radius I was having with the other problems.
Thanks alot!

Yea, I forgot the 2 in the denominator of the limit.