Determine if the series n=2 to inf. of 1/ln(n) converges or diverges Ok so first I tried the limit test (the simple one) and found that it was 0 which was not helpful at all. Then I tried the integral test. It came out to be (integral)1/ln(n)=n/ln(n) + n/(ln(n))^2 + 2(integral from 2 to infin.) 1/(ln(n))^3. I was thinking of possibly doing a direct comparison test, but I have no clue what to compare it to. So then I tried the ratio test. That also failed, because the limit of the absolute value of the ratio was equal to 1 thus inconclusive and leaving me back where I started. I have no idea how else to approach this problem. I am hoping that I maybe just messed up my integration. If anyone has a clue how to approach this that would be great.