I'm trying to determine the interval of convergence for the series:

Using , this simplifies:

According to my solution manual, this is incorrect. The limit

Where am I going wrong?

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- July 19th 2010, 11:25 AMadkinsjrInterval of Convergence
I'm trying to determine the interval of convergence for the series:

Using , this simplifies:

According to my solution manual, this is incorrect. The limit

Where am I going wrong? - July 19th 2010, 12:37 PMelim
The calculation should be:

- July 19th 2010, 01:12 PMAlso sprach Zarathustra
lim |x(n+2)/(n+1)|=|x*lim (n+2)/(n+1)|=|x|*1

For the convergence you need:

|x|<1

Now check for x=1 and x=-1 - July 19th 2010, 01:15 PMadkinsjr
- July 19th 2010, 01:18 PMadkinsjr
- July 19th 2010, 01:37 PMDefunkt
- July 19th 2010, 01:41 PMadkinsjr
I think I've got it now.

The sequence can be written as

That seems right. - July 19th 2010, 01:48 PMadkinsjr
- July 19th 2010, 01:52 PMDefunkt
Oh, you're right; my bad. Looks like you just missed the term from the numerator of the first fraction.

- July 19th 2010, 05:49 PMHallsofIvy
The first thing I would do is simplify to .

The series you have is simply . - July 19th 2010, 05:55 PMAlso sprach Zarathustra
hmmm.... I don't know about this simplification...

- July 19th 2010, 05:58 PMPlato
- July 19th 2010, 06:04 PMAlso sprach Zarathustra
Maybe it because of the night, I don't know! Anyway...

{2*4*6...*(n+1)}*{1*3*5*7*...*n} =(n+1)!

Edit: ooops(again!) I have not noticed that is not only the even numbers!

Sorry! - July 19th 2010, 08:07 PMadkinsjr
- July 20th 2010, 04:18 AMHallsofIvy