If \[S=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-\frac{1}{4.5}+....+\infty ,\] then \[{{e}^{S}}=\] [MP PET 1999]

\[{{\log }_{e}}\left( \frac{e}{4} \right)\]

\[{{\log }_{e}}\left( \frac{4}{e} \right)\]

If \[S=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-\frac{1}{4.5}+....+\i

1.	If \[S=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-\frac{1}{4.5}+....+\infty ,\] then \[{{e}^{S}}=\] [MP PET 1999]
A.	\[{{\log }_{e}}\left( \frac{4}{e} \right)\]
B.	\[\frac{4}{e}\]
C.	\[{{\log }_{e}}\left( \frac{e}{4} \right)\]
D.	\[\frac{e}{4}\]
Answer» C. \[{{\log }_{e}}\left( \frac{e}{4} \right)\]

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If \[S=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-\frac{1}{4.5}+....+\infty ,\] then \[{{e}^{S}}=\] [MP PET 1999]

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