Question Number 196485 by SANOGO last updated on 25/Aug/23
$$\underset{{k}={o}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}} \:=? \\ $$
Commented by mr W last updated on 25/Aug/23
$$=\mathrm{1}−{mod}\left({n},\mathrm{2}\right) \\ $$
Answered by Mathspace last updated on 27/Aug/23
$$=\frac{\mathrm{1}−\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{\mathrm{2}}=\frac{\mathrm{1}+\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}} \\ $$$${so}\:{for}\:{n}=\mathrm{2}{p}\:\Rightarrow{s}=\mathrm{1} \\ $$$${and}\:{for}\:{n}=\mathrm{2}{p}+\mathrm{1}\:\Rightarrow{s}=\mathrm{0} \\ $$
Commented by SANOGO last updated on 27/Aug/23
$${ok}\:{thank}\:{you} \\ $$