- #1

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**Homework Statement**

Does it converge or diverge?

Sum n=0 to infinity : (n/(n+1))^(n^2)

**The attempt at a solution**

I know I need to use the root test.

But what I get is ...

Limit to infinity : (n/(n+1))^n

It seems that the n/(n+1) would go to 1 because when you multiply the top and bottom by n^-1 to get 1/(1+1/n) the 1/n goes to zero and you have 1/1. 1^n is 1, and according to the root test, it is inconclusive. However, the series converges and apparently the limit goes to 1/e, but I'm not sure how.

Also, does the latex syntax not work in preview mode or something?