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?

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- May 10th 2010, 02:20 PMp75213Finding 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 PMlilaziz1
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.

- May 10th 2010, 03:38 PMp75213
That's true. But I would still like to know.

- May 10th 2010, 04:08 PMlilaziz1
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.

- May 10th 2010, 07:08 PMboardguy67
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