# Math Help - Finding the Interval and Radius of Convergence

1. ## 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?

2. 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.

3. That's true. But I would still like to know.

4. 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.

5. 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