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Question Number 165815 by SANOGO last updated on 08/Feb/22

deteminer l′expression de g(x)  g(x)=Σ_(n=1) ^(+oo) (((−1)^n )/n)x^n

$${deteminer}\:{l}'{expression}\:{de}\:{g}\left({x}\right) \\ $$$${g}\left({x}\right)=\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}}{x}^{{n}} \\ $$

Answered by puissant last updated on 08/Feb/22

g(x)=−ln(1+x)=ln((1/(1+x)))..

$${g}\left({x}\right)=−{ln}\left(\mathrm{1}+{x}\right)={ln}\left(\frac{\mathrm{1}}{\mathrm{1}+{x}}\right).. \\ $$

Commented by moubiel last updated on 17/Mar/22

cool

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