I found this question online. Being stuck, I posted it here for some help! I have only noticed that the differences of indices of $x$ are in A.P. with common difference $1$. Apart from that I'm clueless. Please suggest something..! I have solved an similar question but it was much easier or obvious.. (The question was, evaluate: $$\sum_{k=1}^{4n} (-1)^{\frac{k(k+1)}2}\cdot k^2.$$ )
But the present question is not easy for me.. So need your help!