\[\frac{1}{2}+\frac{3}{2}\,.\,\frac{1}{4}+\frac{5}{3}.\frac{1}{8}+\frac{7}{4}.\frac{1}{16}+.....\infty =\]

\[\frac{1}{2}+\frac{3}{2}\,.\,\frac{1}{4}+\frac{5}{3}.\frac{1}{8}+\fra

1.	\[\frac{1}{2}+\frac{3}{2}\,.\,\frac{1}{4}+\frac{5}{3}.\frac{1}{8}+\frac{7}{4}.\frac{1}{16}+.....\infty =\]
A.	\[2-{{\log }_{e}}2\]
B.	\[2+{{\log }_{e}}2\]
C.	\[{{\log }_{e}}4\]
D.	None of these
Answer» B. \[2+{{\log }_{e}}2\]

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\[\frac{1}{2}+\frac{3}{2}\,.\,\frac{1}{4}+\frac{5}{3}.\frac{1}{8}+\frac{7}{4}.\frac{1}{16}+.....\infty =\]

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