\[\frac{1}{1\,.\,2}-\frac{1}{2\,.\,3}+\frac{1}{3\,.\,4}-\frac{1}{4\,.\,5}+.....\infty =\] [Roorkee 1992; AIEEE 2003]

\[\frac{1}{1\,.\,2}-\frac{1}{2\,.\,3}+\frac{1}{3\,.\,4}-\frac{1}{4\,.\

1.	\[\frac{1}{1\,.\,2}-\frac{1}{2\,.\,3}+\frac{1}{3\,.\,4}-\frac{1}{4\,.\,5}+.....\infty =\] [Roorkee 1992; AIEEE 2003]
A.	\[{{\log }_{e}}\frac{4}{e}\]
B.	\[{{\log }_{e}}\frac{e}{4}\]
C.	\[{{\log }_{e}}4\]
D.	\[{{\log }_{e}}2\]
Answer» B. \[{{\log }_{e}}\frac{e}{4}\]

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\[\frac{1}{1\,.\,2}-\frac{1}{2\,.\,3}+\frac{1}{3\,.\,4}-\frac{1}{4\,.\,5}+.....\infty =\] [Roorkee 1992; AIEEE 2003]

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