The sum of \[\frac{1}{2}+\frac{1}{3}.\frac{1}{{{2}^{3}}}+\frac{1}{5}.\frac{1}{{{2}^{5}}}+.....\infty \] is [MP PET 1991]

\[{{\log }_{e}}\sqrt{\frac{1}{2}}\]

\[{{\log }_{e}}\sqrt{\frac{3}{2}}\]

The sum of \[\frac{1}{2}+\frac{1}{3}.\frac{1}{{{2}^{3}}}+\frac{1}{5}.\

1.	The sum of \[\frac{1}{2}+\frac{1}{3}.\frac{1}{{{2}^{3}}}+\frac{1}{5}.\frac{1}{{{2}^{5}}}+.....\infty \] is [MP PET 1991]
A.	\[{{\log }_{e}}\sqrt{\frac{3}{2}}\]
B.	\[{{\log }_{e}}\sqrt{3}\]
C.	\[{{\log }_{e}}\sqrt{\frac{1}{2}}\]
D.	\[{{\log }_{e}}3\]
Answer» C. \[{{\log }_{e}}\sqrt{\frac{1}{2}}\]

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The sum of \[\frac{1}{2}+\frac{1}{3}.\frac{1}{{{2}^{3}}}+\frac{1}{5}.\frac{1}{{{2}^{5}}}+.....\infty \] is [MP PET 1991]

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