\[1+\left( \frac{1}{2}+\frac{1}{3} \right)\,\frac{1}{4}+\left( \frac{1}{4}+\frac{1}{5} \right)\,\frac{1}{{{4}^{2}}}+\left( \frac{1}{6}+\frac{1}{7} \right)\,\frac{1}{{{4}^{3}}}+....\infty =\]

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

\[1+\left( \frac{1}{2}+\frac{1}{3} \right)\,\frac{1}{4}+\left( \frac{1

1.	\[1+\left( \frac{1}{2}+\frac{1}{3} \right)\,\frac{1}{4}+\left( \frac{1}{4}+\frac{1}{5} \right)\,\frac{1}{{{4}^{2}}}+\left( \frac{1}{6}+\frac{1}{7} \right)\,\frac{1}{{{4}^{3}}}+....\infty =\]
A.	\[{{\log }_{e}}(2\sqrt{3})\]
B.	\[2\,\,{{\log }_{e}}2\]
C.	\[{{\log }_{e}}2\]
D.	\[{{\log }_{e}}\left( \frac{2}{\sqrt{3}} \right)\]
Answer» B. \[2\,\,{{\log }_{e}}2\]

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\[1+\left( \frac{1}{2}+\frac{1}{3} \right)\,\frac{1}{4}+\left( \frac{1}{4}+\frac{1}{5} \right)\,\frac{1}{{{4}^{2}}}+\left( \frac{1}{6}+\frac{1}{7} \right)\,\frac{1}{{{4}^{3}}}+....\infty =\]

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