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Question Number 197349 by SANOGO last updated on 14/Sep/23

$$calcul$$$$\underset{n=1}{\sum ^{+oo}}{(-1)}^n\frac{2n+1}{n(n+1)}$$

Answered by MM42 last updated on 14/Sep/23

$$\frac{2n+1}{n(n+1)}=\frac{1}{n}+\frac{1}{n+1}$$$$s_n=-(\frac{1}{1}+\frac{1}{2})+(\frac{1}{2}+\frac{1}{3})-(\frac{1}{3}+\frac{1}{4})-...$$$$s_n=-1\pm \frac{1}{n+1}\Rightarrow s={lim}_{n\to \mathrm{\infty }}{s}_n=-1$$$$$$

Commented by SANOGO last updated on 14/Sep/23

$$merci$$

Commented by MathematicalUser2357 last updated on 16/Sep/23

$$ronaldo$$

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