Let-S-n-k-1-4n-1-k-k-1-2-k-2-Then-S-n-can-take-the-value-s-1-1056-2-1088-3-1120-4-1332-

Question Number 31864 by rahul 19 last updated on 16/Mar/18

Let S_n = Σ_(k=1) ^(4n) (−1)^((k(k+1))/2) k^2 . Then S_n can take the value(s) 1) 1056 2) 1088 3) 1120 4) 1332.

$${Let}\:{S}_{{n}} =\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{4}{n}} {\sum}}\left(−\mathrm{1}\right)^{\frac{{k}\left({k}+\mathrm{1}\right)}{\mathrm{2}}} {k}^{\mathrm{2}} . \\ $$$${Then}\:{S}_{{n}} \:{can}\:{take}\:{the}\:{value}\left({s}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{1056} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{1088} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{1120} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{1332}. \\ $$

Answered by Tinkutara last updated on 16/Mar/18