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Question Number 196485 by SANOGO last updated on 25/Aug/23

Σ_(k=o) ^n (−1)^k  =?

$$\underset{{k}={o}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} \:=? \\ $$

Commented by mr W last updated on 25/Aug/23

=1−mod(n,2)

$$=\mathrm{1}−{mod}\left({n},\mathrm{2}\right) \\ $$

Answered by Mathspace last updated on 27/Aug/23

=((1−(−1)^(n+1) )/2)=((1+(−1)^n )/2)  so for n=2p ⇒s=1  and for n=2p+1 ⇒s=0

$$=\frac{\mathrm{1}−\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{\mathrm{2}}=\frac{\mathrm{1}+\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}} \\ $$$${so}\:{for}\:{n}=\mathrm{2}{p}\:\Rightarrow{s}=\mathrm{1} \\ $$$${and}\:{for}\:{n}=\mathrm{2}{p}+\mathrm{1}\:\Rightarrow{s}=\mathrm{0} \\ $$

Commented by SANOGO last updated on 27/Aug/23

ok thank you

$${ok}\:{thank}\:{you} \\ $$

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