5.4.1

[STARTS AT 4:45]

Instructor: All right, determine whether this series converges or diverges. Same setup-- let's see if we can compare this to something. Well, I can definitely pull the same trick that we did last time or a couple of these ago. The sum from 1 to infinity of n over n cubed-- OK, that is definitely true for all n greater than or equal to 1. 

But then this is also equal to the sum from 1 to infinity of 1 over n squared. And that's just true in general. And I can cancel that. Now because that's true always, this series-- since the series n equals 1 to infinity of 1 over n squared converges, that means that the sum from n equals 1 to infinity of in over n cubed plus n plus 1 converges. 

Because term by term, it is less than or equal to what we've now determined converges. So if we can somehow compare it to a p-series or a geometric, that is fantastic. Those are the only ones that we really are completely familiar with at this point that converge.