Very confused about the following:

Find the radius of convergence and interval of convergence of the series.

http://www.webassign.net/cgi-bin/sym...%2F%28n%2B6%29

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- Jul 1st 2010, 07:49 PMabel2Radius and Interval of Convergence
Very confused about the following:

Find the radius of convergence and interval of convergence of the series.

http://www.webassign.net/cgi-bin/sym...%2F%28n%2B6%29 - Jul 1st 2010, 09:09 PMJhevon
- Jul 2nd 2010, 07:35 AMabel2
Ok so using the ratio test where

Then we have

Simplifying, we get

Then I get

and therefore converges.

Still not sure how to solve for the center point and find the two endpoints. I'm left with x = -1

I apologize in advance for my crappy latex. The higher parentheses are superscripts. And I'm not sure about the absolute value cmd. - Jul 2nd 2010, 09:12 AMabel2
Well that can't be right. 1/n = infinity. But I am sure this equation converges. Somehow I think I cancelled out the n's incorrectly. Should have ended up with a L'Hospital's method and gotten 1/1 is my suspicion. But if that is the case, wouldn't I just solve for x giving 0? But then I have no idea how to get the endpoints unless they are -1<x<1 where x=0. With radius of 1.

- Jul 2nd 2010, 09:57 AMskeeter

... radius of convergence is r = 1

checking the endpoints ...

when

... alternating series that converges

when

... series diverges

interval of convergence is