>> In dealing with sequences at this point, two fundamental questions are emerging. One is whether or not the series converges, so whether or not it converges or diverges. And if it converges, to what value does it converge. Now it should make some sense [Inaudible] if it's going converge that at some point the items in the series, the items that we're adding, need to get really, really small. They need to approach 0. And a fancy watch of saying that is like this. Given a summation that is in this form, if the limit as it approaches infinity as A of N is not equal to 0. If these values -- if the value of the nth term, as N approaches infinity, is not approaching 0 or is not 0, then the series diverges. And it's pretty easy to see with an example if we're talking about this, and it's 5 plus 10 plus 15, gee, the values are getting larger and larger, this can't possibly converge. So this diverges because the limit as N approaches infinity of 5 N is equal to infinity. In fact, I could change it a little bit, I could make it into a constant situation like this. I could say okay, the limit as -- excuse me, the sum as N runs from 1 to infinity would be -- let's see, would end up being 5 plus 5 plus 5 plus 5 and so on. But the point is -- so it would be this. But it diverges because the limit as N approaches infinity of just the number 5 would be 5. You see? It's always going to be 5, the values will be. And because the value doesn't go down to 0, you see, it can't possibly converge.