00:01
For this problem, we'll use the squeeze theorem.
00:03
So the thing that kind of gets tricky with this a -n term is this cosine squared of n.
00:10
So the cosine squared of n is the troublemaker here.
00:14
And hopefully it's something that's bounded.
00:16
And if it is, which is the case here, then you can use the squeeze theorem.
00:21
So we bound this thing that's giving us some trouble.
00:24
So this is cosine squared of n.
00:26
So that's going to be bigger than or equal to zero and less than or equal to 1.
00:33
It can't be a negative number because this is cosine squared.
00:38
Okay, so this is going to be something that's true for all n.
00:43
And we can divide by 2 to the n and it's not going to change these bounds either because 2 to the n is always going to be some positive number.
00:52
So dividing by a positive number or multiplying by a positive number, we don't have to worry about flipping these things at all...