A) \[2{{\log }_{e}}\frac{4}{5}\]
B) \[{{\log }_{e}}\frac{5}{4}\]
C) 1
D) 0
Correct Answer: D
Solution :
\[{{\log }_{e}}\frac{4}{5}+\frac{1}{4}-\frac{1}{2}{{\left( \frac{1}{4} \right)}^{2}}+\frac{1}{3}{{\left( \frac{1}{4} \right)}^{3}}+....\] = \[{{\log }_{e}}\frac{4}{5}+{{\log }_{e}}\left( 1+\frac{1}{4} \right)={{\log }_{e}}\frac{4}{5}+{{\log }_{e}}\frac{5}{4}=0\].
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