Please I need help :/
Does the series $$\large \sum_{n=1}^{\infty}\frac{n^{n}}{3^{(n^{2})}}$$ converge or diverge, which test shows this?

Question

Please I need help :/
Does the series $$\large \sum_{n=1}^{\infty}\frac{n^{n}}{3^{(n^{2})}}$$ converge or diverge, which test shows this?

kainui · Answer

http://www.wolframalpha.com/input/?i=sum+from+1+to+infinity+%28n%2F3^n%29^n So it says it converges by the ratio test, but I forget what that is. I'm sure you can figure it out and use this as a tool to help you study.

terenzreignz · Answer

Oh what fun ^_^

terenzreignz · Answer

@Ray10 Are you in fact still here?

ray10 · Answer

I shall look into that site thank you! :)

ray10 · Answer

@terenzreignz yes I am :)

terenzreignz · Answer

Pity, too late :D
Never mind the ratio test, use the bloody Root Test,

Every factor in the summand is raised to n (or a variant thereof)

ray10 · Answer

:D Oh thank you @terenzreignz !!
yes a bit late, sorry >.<
the root test! :D