Calculus II - Series Comparison Test Problems

[invasmani]

Homework Statement

I have two relatively similar problems:

1.) Sigma n=1 to infinity ((ln n)^3 / n^2)
2.) Sigma n=1 to infinity (1 / sqrt(n) * (ln n)^4)

I'm to prove their convergence or divergence using either the direct comparison test or the limit comparison test.

I understand both comparison tests, however, I am very much stumped on how to determine a working bn for the problems.

The Attempt at a Solution

I've tried using a known p-series, such as 1/(n^2) for problem #1, which is convergent. However, that p-series is not greater than the an in this case.

I'd appreciate any sort of direction on this.

 

[Dick]

ln(n) grows more slowly than any power x^p for p>0. Can you suggest an interesting value of p that's relevant for 1) or 2)?