When doing this problem, we have to get this into partial fractions and figure out each individual one. So eighty n / 2 N -1 ^2 * 2 N plus one squared. So this is going to be a / 2 N -1 + b / 2 N -1 ^2 plus C / 2 N plus 1 + d / 2 N plus one squared. So then getting a common denominator, we'd have 80 N equaling a * 2 N -1 * 2 N plus 1 ^2 + b * 2 N plus 1 ^2 + C times 2N plus 12 N -1 ^2 + d * 2 N -1 ^2. So from there I'm going to try to see if we could get things to cancel. If I let N equal 1/2 positive 1/2, then this term would go to 0 every time we see it, so that 2 N -1 would cancel this 2 N -1 would cancel, this 2 N -1 would cancel, and we'd end up with 80 * 1/2 because the N was 1/2 equaling b * 2 * 1/2 + 1 ^2. So I'd have 40 equaling 2 * 1/2 is 1 + 1 is 22, squared is 4, so my B would be 10. I'm going to do that same concept, but this time I'm going to let N equal negative 1/2 if that's the case. If N is negative 1/2, this time the 2N plus ones are going to cancel. SO2N plus 1/2 N plus 1/2 N plus one. And what will happen then is we'd have 80 times negative 1/2 equaling d * 2 times negative 1/2 - 1 ^2. So this is -1 -, 1 negative 2 ^2 would be 4, so 4D equal -40. So D equal -10. So we're going to get 10 / 10 two N -1 quantity squared -10 / 2 N plus one quantity squared. Now, we still have that A and that C, so we don't know that that's really going to be totally factored yet. But if I thought about getting a common denominator here and just seeing if that's what 80 N would equal it, we might get lucky. We might realize that this may or may not be the correct thing. So if I just look at I can't move over any further, I'm OK, let's see. We'll highlight this and move it over a little and OK, there we go. So we might get lucky and realize that A and C are zero. I don't know that we will. We have to look and find out. If I just look at these first two terms, I'd get 10 times four n ^2 + 4 N plus 1 - 10 * 4 N squared -4 N plus one over the two n - 1 ^2 times the two n + 1 ^2. If we look here, the +40 N squared -40 N squared are going to cancel the +40 N and the -10 * -4 N is going to give us a +40 N. So that gives me the 80 N That's a good thing. And then the +10 and the -10 cancel. So then we can see that this A and the C both have to be 0. So now all we're really caring about is this 10 / 2 N -1 ^2 portion. So we want 10 / 2 N -1 ^2 - 10 / 2 N plus one squared. So 10 / 2 N -1 ^2 -10 / 2 N plus one squared. And this is going to be a summation of N equals something to Infinity. What was the something? The something was one. So now if we put in N equal 1, we can see that we get 10 / 1 two times 1 -, 1 is 1 ^2 - 10 / 2 * 1, one plus one 3 ^2 9. And if we put in the next term 2 4 -, 1, three squared is 9. And if we put in the next term, 2 * 3 is 6 + 1, seven squared is 49. So we can see that it's going to be the second term of the one -10 ninths will cancel with the first term of the other. So when we look at this now, what we have is we have this really equaling 10 / 1 -, 10 / 2 N plus one squared. And we want to know what happens to that as N goes out to Infinity, because the limit was going to Infinity. Well, 10 over something really, really big is going to be really, really small. So that's just going to give us that 10 / 1 in the beginning.