The sum to infinity of the given series \[\frac{1}{n}-\frac{1}{2{{n}^{2}}}+\frac{1}{3{{n}^{3}}}-\frac{1}{4{{n}^{4}}}+....\] is [MP PET 1994]

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

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

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

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

The sum to infinity of the given series \[\frac{1}{n}-\frac{1}{2{{n}^{

1.	The sum to infinity of the given series \[\frac{1}{n}-\frac{1}{2{{n}^{2}}}+\frac{1}{3{{n}^{3}}}-\frac{1}{4{{n}^{4}}}+....\] is [MP PET 1994]
A.	\[{{\log }_{e}}\left( \frac{n+1}{n} \right)\]
B.	\[{{\log }_{e}}\left( \frac{n}{n+1} \right)\]
C.	\[{{\log }_{e}}\left( \frac{n-1}{n} \right)\]
D.	\[{{\log }_{e}}\left( \frac{n}{n-1} \right)\]
Answer» B. \[{{\log }_{e}}\left( \frac{n}{n+1} \right)\]

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The sum to infinity of the given series \[\frac{1}{n}-\frac{1}{2{{n}^{2}}}+\frac{1}{3{{n}^{3}}}-\frac{1}{4{{n}^{4}}}+....\] is [MP PET 1994]

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