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k-1-n-1-k-k-




Question Number 121041 by bramlexs22 last updated on 05/Nov/20
 Σ_(k=1) ^n  (−1)^k .k =?
$$\:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\left(−\mathrm{1}\right)^{\mathrm{k}} .\mathrm{k}\:=?\: \\ $$
Answered by Dwaipayan Shikari last updated on 05/Nov/20
−1+2−3+4−5+6−7+8−...=(n/2)
$$−\mathrm{1}+\mathrm{2}−\mathrm{3}+\mathrm{4}−\mathrm{5}+\mathrm{6}−\mathrm{7}+\mathrm{8}−…=\frac{{n}}{\mathrm{2}} \\ $$

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