 Hello, and welcome to a screencast today about absolute convergence. All right, today we're asking the question, does the series converge absolutely, not just converge, converge absolutely. So our series is n goes from 1 to infinity of negative 1 to the n plus 1 all over n squared. Okay, now by the alternating series test, because this thing's definitely going to be alternating with this negative 1 to the n plus 1, we do know that it converges, okay, so that's nice. But our question is, does it converge absolutely? So that's where we need to look at the series of the absolute value of this stuff. So let's look at n goes from 1 to infinity, and then we want the absolute value of negative 1 to the n plus 1 all over n squared. Okay, so what's this absolute value going to do for us? Well, it takes anything that's negative and changes it to positive. So then this numerator is going to be alternating between negative 1 and positive 1. So these absolute values are just going to make it just a strict positive 1. So I've now got this series n goes from 1 to infinity of 1 over just n squared. Okay, well that's a p-series if you remember what that is. So p is 2, this thing's obviously going to converge. Otherwise you can do an integral test on this one, or you know, there's probably lots of other things too. But we know that this series converges. So because that's the same thing as the absolute value of our original series, that means our series negative 1 to the n plus 1 all over n squared converges absolutely. And there we go. Okay, so basically absolute convergence, it gives us a little bit stronger of a case of convergence, and then all we really have to do then is just test the absolute value of your function. So it's really not much more to test for this stuff, but like I said it gives you a much stronger case of convergence. Alright, thank you for watching.