series- Real Analysis

• February 13th 2010, 06:29 PM
hebby
series- Real Analysis
$(-1)^n n^n/ (n+1)to the power (n+1).$
I dont know how to show if it converges or diverges?

Any ideas?
• February 13th 2010, 07:20 PM
felper
did you try the Leibniz test?
• February 13th 2010, 07:21 PM
hebby
I need to use the AbeL test...i think, but im not sure how to use it
• February 15th 2010, 06:59 PM
Drexel28
Quote:

Originally Posted by hebby
$(-1)^n n^n/ (n+1)to the power (n+1).$
I dont know how to show if it converges or diverges?

Any ideas?

$\frac{n^n(-1)^n}{(n+1)^{n+1}}=\frac{(-1)^n}{n+1}\cdot\left(1+\frac{1}{n}\right)^n\to 0\cdot e$?
• February 15th 2010, 07:10 PM
hebby
so the series converges to 0?
• February 15th 2010, 07:11 PM
Drexel28
Quote:

Originally Posted by hebby
so the series converges to 0?

Uh...yes.
• February 16th 2010, 08:03 PM
hebby
Quote:

Originally Posted by Drexel28
Uh...yes.

will let be conditional convergence as the abs. values will make 1/n+1 divergent?
• February 16th 2010, 08:14 PM
icemanfan
Quote:

Originally Posted by hebby
will let be conditional convergence as the abs. values will make 1/n+1 divergent?

Are we evaluating this?

$\sum_{n=1}^\infty \frac{(-1)^n}{n+1}\cdot\left(1+\frac{1}{n}\right)^n$
• February 16th 2010, 08:17 PM
hebby
yes
• February 16th 2010, 08:30 PM
icemanfan
Quote:

Originally Posted by hebby
yes

Then it converges conditionally, as you stated.