 In this video, we provide the solution to question number two for practice exam number four for math 12-20, in which case we have to compute the limit of the sequence where A is given as negative one to the N times N plus two over N. So when I look at this, the first thing that gives me some concern here is gonna be this negative one to the N. So this is an example of an alternating sequence. Now an alternating sequence is convergent only if the limit goes to zero. And I'm not talking about an alternating series, I'm talking about an alternating sequence. The sequence will alternate back and forth between positive, negative, positive, negative, positive, negative. So if you ignore the negative one for a moment, if you ignore that, notice this thing is gonna go off towards N plus two over N since it's a balanced ratio, this is gonna go off towards their coefficients which is just one in that situation. But it's one times this negative one to the N. That's where this thing would converge to. So this is gonna, the limit here wants to be negative one to the N, which of course, if you're allowing N to be infinity, right? You're getting, you get the limit would be negative one to the infinity. That's not a number. If it's switching back equally often between one and negative one, there is no limit here. This is an example of a divergent sequence here. An alternating sequence can only be convergent if it's limits one. And this thing is not getting closer to, sorry. An alternating sequence is convergent only if it's limit is zero. That's what I meant to say. This thing is not getting close to zero. It's getting close to one and negative one. And that makes it divergent.