\[\frac{2}{1}\,.\,\frac{1}{3}+\frac{3}{2}.\frac{1}{9}+\frac{4}{3}.\frac{1}{27}+\frac{5}{4}.\frac{1}{81}+......\infty =\]

\[\frac{1}{2}-{{\log }_{e}}\frac{2}{3}\]

\[\frac{1}{2}+{{\log }_{e}}\left( \frac{2}{3} \right)\]

\[\frac{2}{1}\,.\,\frac{1}{3}+\frac{3}{2}.\frac{1}{9}+\frac{4}{3}.\fra

1.	\[\frac{2}{1}\,.\,\frac{1}{3}+\frac{3}{2}.\frac{1}{9}+\frac{4}{3}.\frac{1}{27}+\frac{5}{4}.\frac{1}{81}+......\infty =\]
A.	\[\frac{1}{2}-{{\log }_{e}}\frac{2}{3}\]
B.	\[-{{\log }_{e}}\frac{2}{3}\]
C.	\[\frac{1}{2}+{{\log }_{e}}\left( \frac{2}{3} \right)\]
D.	None of these
Answer» B. \[-{{\log }_{e}}\frac{2}{3}\]

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\[\frac{2}{1}\,.\,\frac{1}{3}+\frac{3}{2}.\frac{1}{9}+\frac{4}{3}.\frac{1}{27}+\frac{5}{4}.\frac{1}{81}+......\infty =\]

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