Hey camorris.
The big hint is knowing that (-1)^2r = 1 for all integer values of r and (-1)^(2r+1) = -1 again for all integer values of r.
Can some one please help me with this question? I have answered it already although do not understand each stage. Such as the first 8 for example. Rather than carry on I would like some clarification on how I got there and why.