Please help give me some clue for this problem.
The Problem: Determine whether or not the following series converges. Be sure to name the test you use to make your decision and show it.
Given: n=2∑∞n(lnn)21
Looking at the possible tests that I know such as, geometric series, P-series, harmonic series, comparison test, ratio test, root test, alternating series, and integral test, I can only see that the integral test is probably most fit for this problem. But if I am correct to use the integral test, then am I suppose to use "the integration by part" for solving the integral part of it? I tried the "integration by part" but it did not seem right in my work regardless if I assign u=x1 and dv=(lnn)21 or vice versa. Please tell me which test would lead me to determine the convergence or divergence of this series.
Thanks,
The Problem: Determine whether or not the following series converges. Be sure to name the test you use to make your decision and show it.
Given: n=2∑∞n(lnn)21
Looking at the possible tests that I know such as, geometric series, P-series, harmonic series, comparison test, ratio test, root test, alternating series, and integral test, I can only see that the integral test is probably most fit for this problem. But if I am correct to use the integral test, then am I suppose to use "the integration by part" for solving the integral part of it? I tried the "integration by part" but it did not seem right in my work regardless if I assign u=x1 and dv=(lnn)21 or vice versa. Please tell me which test would lead me to determine the convergence or divergence of this series.
Thanks,