# Finding the Interval and Radius of Convergence

#### p75213

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?

#### lilaziz1

It really doesn't matter because $$\displaystyle \sum_{n=0}^{\infty} \frac{1}{n+1}$$ behaves like $$\displaystyle \sum_{n=0}^{\infty} \frac{1}{n}$$ by the limit camparison test.

#### p75213

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

#### lilaziz1

I don't think it can be $$\displaystyle \sum_{n=0}^{\infty} \frac{1}{n} -1$$ because if you make it into an improper fraction, you get $$\displaystyle \sum_{n=0}^{\infty} \frac{1-n}{n}$$ which diverges.

#### 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/calculus/Lecture43-rev.pdf

Hope that helps,
Be well,
T

mr fantastic