# Finding the Interval and Radius of Convergence

• May 10th 2010, 02:20 PM
p75213
Finding the Interval and Radius of Convergence
The equation is: Summation n=1 to inf x^n/(n+1)

When the endpoints are checked at x=1 - 1^n/(n+1) is rewritten as 1/n - 1. Can somebody show me the validity of this?

http://my.thinkwell.com/questionbank.../img/61724.gif
• May 10th 2010, 02:34 PM
lilaziz1
It really doesn't matter because $\sum_{n=0}^{\infty} \frac{1}{n+1}$ behaves like $\sum_{n=0}^{\infty} \frac{1}{n}$ by the limit camparison test.
• May 10th 2010, 03:38 PM
p75213
That's true. But I would still like to know.
• May 10th 2010, 04:08 PM
lilaziz1
I don't think it can be $\sum_{n=0}^{\infty} \frac{1}{n} -1$ because if you make it into an improper fraction, you get $\sum_{n=0}^{\infty} \frac{1-n}{n}$ which diverges.
• May 10th 2010, 07:08 PM
boardguy67
Hi p75213...are you a Stargate fan? (if you get that, you are :))

Anyway, your problem is in the form of the ratio test for convergence, which basically lets you compare your series to a geometric series to determine it's behavior. I think you'll find your proof here.

http://www.math.scar.utoronto.ca/cal...ture43-rev.pdf

Hope that helps,
Be well,
T