\[\frac{x-1}{(x+1)}+\frac{1}{2}\,.\,\frac{{{x}^{2}}-1}{{{(x+1)}^{2}}}+\frac{1}{3}\,.\,\frac{{{x}^{3}}-1}{{{(x+1)}^{3}}}+......\infty =\]

\[\frac{x-1}{(x+1)}+\frac{1}{2}\,.\,\frac{{{x}^{2}}-1}{{{(x+1)}^{2}}}+

1.	\[\frac{x-1}{(x+1)}+\frac{1}{2}\,.\,\frac{{{x}^{2}}-1}{{{(x+1)}^{2}}}+\frac{1}{3}\,.\,\frac{{{x}^{3}}-1}{{{(x+1)}^{3}}}+......\infty =\]
A.	\[{{\log }_{e}}x\]
B.	\[{{\log }_{e}}(1+x)\]
C.	\[{{\log }_{e}}(1-x)\]
D.	\[{{\log }_{e}}\frac{x}{1+x}\]
Answer» B. \[{{\log }_{e}}(1+x)\]

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\[\frac{x-1}{(x+1)}+\frac{1}{2}\,.\,\frac{{{x}^{2}}-1}{{{(x+1)}^{2}}}+\frac{1}{3}\,.\,\frac{{{x}^{3}}-1}{{{(x+1)}^{3}}}+......\infty =\]

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