💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Numerade Educator

Like

Report

Problem 22 Medium Difficulty

Determine whether the series is convergent or divergent.
$ \displaystyle \sum_{n = 2}^{\infty} \frac {\ln n}{n^2} $

Answer

diverges

Discussion

You must be signed in to discuss.

Clayton C.

January 13, 2018

There is a mistake late in the problem. The P-series test says that for P>1, the series is CONVERGENT, so the overall series converges, not diverges.

Video Transcript

for the sake of an easier explanation, I'm going to split this Siri's by taking its first term out explicitly. If we take out Alan of two over two squared and add that the rest of the Siri's No should not be three there, that should be an end. What this allows us to do is say, well, for n equals three and Greater Ellen of n is created one, since the defense greater than E we get that. What this means is that from n equals three to Infinity, Allen of End Over and Squared is actually gonna be strictly greater than just the same serious for one over and scored. And as we know frumpy Siri's we have won over and to the P and P is greater than one. Then we have a divergence, Siri's. So we end up with this divergent and this's some number. So comparison test tells us that if we have the Siri's greater than another Siri's, and that smaller Siri's converges bear diverges than the other serious de bridges as well. So in this case, are smaller. Siri's is this diversion one. So our other Siri's conclusion someone's here, Vergis