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

\[{{\log }_{e}}\left( 1-\frac{1}{x} \right)\]

\[{{\log }_{e}}\left( 1+\frac{1}{x} \right)\]

\[{{\log }_{e}}\left( \frac{x}{x+1} \right)\]

\[\frac{1}{x+1}+\frac{1}{2\,{{(x+1)}^{2}}}+\frac{1}{3\,{{(x+1)}^{3}}}+

1.	\[\frac{1}{x+1}+\frac{1}{2\,{{(x+1)}^{2}}}+\frac{1}{3\,{{(x+1)}^{3}}}+....\infty =\]
A.	\[{{\log }_{e}}\left( 1+\frac{1}{x} \right)\]
B.	\[{{\log }_{e}}\left( 1-\frac{1}{x} \right)\]
C.	\[{{\log }_{e}}\left( \frac{x}{x+1} \right)\]
D.	None of these
Answer» B. \[{{\log }_{e}}\left( 1-\frac{1}{x} \right)\]

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

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