Convergence of alternating series ln n/n?

Question

I know that this series converges, but I need an explanation of this. The series is from n=1 to infinity of (-1)^n+1(ln (n)/n)

Answer 1

Using L'Hopital's Rule
ln(n)/n = 0
lim n --> infinity
Also | ln(n)/n| >| ln (n+1)/(n+1)|
Thus the condition for convergence is met.

Answer 2

It converges by The Alternating Series Test.