Finding the Interval and Radius of Convergence

Nov 2009
76
1
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?

 
Mar 2010
107
14
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.
 
Nov 2009
76
1
That's true. But I would still like to know.
 
Mar 2010
107
14
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.