Question

Determine whether the following series converges or diverges

Answer 1

\[\sum_{n=1}^{\infty} n e ^{n ^{2}}\]

Answer 2

do I use the integral test?

Answer 3

you could, but you can use the divergent test.
Lim n->inf (n e^n^2) = inf, which is not 0, so the series diverges

Answer 4

Ohhhhh so e^n basically is infinity. That simple?

Answer 5

yes, but remember that we have (n e^n^2) in this case

Answer 6

yeah but infinity sqrd is still going to be infinity

Answer 7

yes

Answer 8

Ok thank you :)