1. ## series- Real Analysis

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

Any ideas?

2. did you try the Leibniz test?

3. I need to use the AbeL test...i think, but im not sure how to use it

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

Any ideas?
$\displaystyle \frac{n^n(-1)^n}{(n+1)^{n+1}}=\frac{(-1)^n}{n+1}\cdot\left(1+\frac{1}{n}\right)^n\to 0\cdot e$?

5. so the series converges to 0?

6. Originally Posted by hebby
so the series converges to 0?
Uh...yes.

7. Originally Posted by Drexel28
Uh...yes.
will let be conditional convergence as the abs. values will make 1/n+1 divergent?

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

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n}{n+1}\cdot\left(1+\frac{1}{n}\right)^n$

9. yes

10. Originally Posted by hebby
yes
Then it converges conditionally, as you stated.