Question

Does the series converge or diverge?

(n+ 1/n)^n

Answer 1

when I distribute the n does (1/n) become (1/n^n)?

Answer 2

\[
\sum_n\left(\frac{n+1}{n}\right)^n \to \infty
\]

Answer 3

awesome so it does diverge

Answer 4

Yes. If you meant:
\[
\sum_n\left(n+\frac{1}{n}\right)^n\to \infty
\]It still diverges.

When asking the question, could you put up what you got as an answer? Just so I don't get a warning for 'giving answers.'

Thanks.

Answer 5

sure:)