1. The problem statement, all variables and given/known data Determine whether Ʃ(n from 1 to infinity) ln(n)/n^3 converges or diverges using the limit comparison test. 2. Relevant equations I must use the limit comparison test to solve this problem-not allowed to use other tests. 3. The attempt at a solution I know that the series converges, because the integral test shows that the the integral does converge to a specific value. This proves that Ʃ(n from 1 to infinity) ln(n)/n^3 converges. However, I have to solve this problem with the limit comparison test. Now my best results so far is that the rate of increase of the natural log function is slower than the rate of increase of any power function with the exponent greater than 0, so I believe that the series ln(n)/n^3 mimics the series 1/n^3. This series, 1/n^3, is the p-series whose convergence can easily be determined by looking at the exponent. If n>1, the series converges. If n≤1, the series diverges. The same principle applies to the series ln(n)/n^k: It appears that the series converges whenever k>1 and diverges when k≤1. But how can the limit comparison test be employed? There just seems to be no suitable function to compare ln(n)/n^3 with. Please help?