How do I find the sum of the series -1^2-2^2+3^2+4^2-5^2… upto 4n terms? – math.stackexchange.com

I tried by giving $$ S = \sum_{k=0}^{n-1} \left((4k+3)^2+(4k+4)^2-(4k+1)^2-(4k+2)^2\right) $$ but I am stuck here. I have no idea what to do next. The answer in my book says 4n(n+1). How can I get ...

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