Please help me with this Calculus 2 series question I am stuck on

Question

Use the Integral Test to determine whether the series is convergent or divergent.

∞
ne−12n
n = 1

ok so I know this is an integral test

i know i have to take the derative

and I got -12e^-12x+e^-12x, however I do not know what to do next

Answer 1

No, you need to integrate xe^-12x from 1 to ∞ and if this integral converges then the series converges. In this case the integral has a factor of e^-12x goes to 0 for large x and is bounded at x=1; therefore, the integral and the series converge.