The sum of the series \[\frac{2}{1}.\frac{1}{3}+\frac{3}{2}.\frac{1}{9}+\frac{4}{3}.\frac{1}{27}+\frac{5}{4}.\frac{1}{81}+......\infty \] is equal to

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

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

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

\[{{\log }_{e}}3+{{\log }_{e}}2\]

The sum of the series \[\frac{2}{1}.\frac{1}{3}+\frac{3}{2}.\frac{1}{9

1.	The sum of the series \[\frac{2}{1}.\frac{1}{3}+\frac{3}{2}.\frac{1}{9}+\frac{4}{3}.\frac{1}{27}+\frac{5}{4}.\frac{1}{81}+......\infty \] is equal to
A.	\[{{\log }_{e}}3-{{\log }_{e}}2\]
B.	\[\frac{1}{2}+{{\log }_{e}}3-{{\log }_{e}}2\]
C.	\[\frac{1}{2}+{{\log }_{e}}3+{{\log }_{e}}2\]
D.	\[{{\log }_{e}}3+{{\log }_{e}}2\]
Answer» C. \[\frac{1}{2}+{{\log }_{e}}3+{{\log }_{e}}2\]

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The sum of the series \[\frac{2}{1}.\frac{1}{3}+\frac{3}{2}.\frac{1}{9}+\frac{4}{3}.\frac{1}{27}+\frac{5}{4}.\frac{1}{81}+......\infty \] is equal to

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