I have no idea where to start with this one. I tried finding the limits of each, finding the partial sums, I just don't really know how to prove it
any help would be appreciated
If so, you should cut the left-hand side sum into two parts: the even (the numerator is -1) and the odd terms (it is +1), and then put both sums together.
Another way (this is the same in fact) is summing the terms two by two: write for the left-hand side.