Sum of the convergent infinite series ln(n)/n^2

1. Jan 22, 2009

mathgurl20

1. The problem statement, all variables and given/known data

Find the sum of the series: ln(n)/n^2 from n=1 to infinity.
I already know that it is convergent(at least i hope i am right on that fact)

2. Relevant equations

3. The attempt at a solution
I tried to use geometric series but i can't see anything like that that would work, and i can't see a way to use telescoping. And just starting with n=1 and summing numbers didn't seem to get me anywhere either.

2. Jan 22, 2009

MathematicalPhysicist

You still can use telescoping.
ln((n+1)^(1/(n+1)^2))-ln(n^(1/n^2)), use stolz theorem on this limit to get your answer, btw I am sure you know that but stolz theorem resembles L'hopital theorem.

3. Jan 27, 2009

mathgurl20

Thank you very much :)