Determine whether the series is convergent or divergent

Question

series symbol n=1 to infinity (n^2/(e^(3n))

Answer 1

an+1/an = e^-3 (1 + 2/n + 1/n^2)

that ratio is less than 1, so the series converges.

see

http://www.wolframalpha.com/input/?i=sum+n^2%2Fe^%283n%29

Answer 2

we can't use the ratio test on it. The only thing we know as of now is the integral test.