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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- Jul 19th 2010, 10:25 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? - Jul 19th 2010, 11:37 AMelim
The calculation should be:

- Jul 19th 2010, 12:12 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 - Jul 19th 2010, 12:15 PMadkinsjr
- Jul 19th 2010, 12:18 PMadkinsjr
- Jul 19th 2010, 12:37 PMDefunkt
- Jul 19th 2010, 12:41 PMadkinsjr
I think I've got it now.

The sequence can be written as

That seems right. - Jul 19th 2010, 12:48 PMadkinsjr
- Jul 19th 2010, 12:52 PMDefunkt
Oh, you're right; my bad. Looks like you just missed the term from the numerator of the first fraction.

- Jul 19th 2010, 04:49 PMHallsofIvy
The first thing I would do is simplify to .

The series you have is simply . - Jul 19th 2010, 04:55 PMAlso sprach Zarathustra
hmmm.... I don't know about this simplification...

- Jul 19th 2010, 04:58 PMPlato
- Jul 19th 2010, 05:04 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! - Jul 19th 2010, 07:07 PMadkinsjr
- Jul 20th 2010, 03:18 AMHallsofIvy