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Question Number 163463 by SANOGO last updated on 07/Jan/22

nature de la serie  Σ_(n=1) ((1/(n+1))+(1/n))

$${nature}\:{de}\:{la}\:{serie} \\ $$$$\underset{{n}=\mathrm{1}} {\sum}\left(\frac{\mathrm{1}}{{n}+\mathrm{1}}+\frac{\mathrm{1}}{{n}}\right) \\ $$

Answered by Ar Brandon last updated on 07/Jan/22

Σ_(n=1) ^∞ ((1/(n+1))+(1/n))=Σ_(n=1) ^∞ ((1/n)+(1/n))−1  =2H_n −1 →divergente

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}+\mathrm{1}}+\frac{\mathrm{1}}{{n}}\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}}+\frac{\mathrm{1}}{{n}}\right)−\mathrm{1} \\ $$$$=\mathrm{2}{H}_{{n}} −\mathrm{1}\:\rightarrow\mathrm{divergente} \\ $$

Commented by SANOGO last updated on 07/Jan/22

merci bien

$${merci}\:{bien} \\ $$

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