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Question Number 197320 by tri26112004 last updated on 13/Sep/23

$$\underset{k=1}{\sum ^n}{(-1)}^{k(k+1)}$$

Answered by Erico last updated on 13/Sep/23

$$\mathrm{\forall }\mathrm{k}\in [1,\mathrm{n}]{(-1)}^{\mathrm{k}(\mathrm{k}+1)}=1$$$$\Rightarrow \underset{\mathrm{k}=1}{\sum ^{\mathrm{n}}}{(-1)}^{\mathrm{k}(\mathrm{k}+1)}=\mathrm{n}$$

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