A) \[{{\log }_{e}}\sqrt{\frac{3}{2}}\]
B) \[{{\log }_{e}}\sqrt{3}\]
C) \[{{\log }_{e}}\sqrt{\frac{1}{2}}\]
D) \[{{\log }_{e}}3\]
Correct Answer: B
Solution :
Sum of \[\frac{1}{2}+\frac{1}{3}.\frac{1}{{{2}^{.3}}}+\frac{1}{5}.\frac{1}{{{2}^{5}}}+....\infty \] = \[\frac{1}{2}\left[ 1+\frac{1}{3}.\frac{1}{{{2}^{2}}}+\frac{1}{5}.\frac{1}{{{2}^{4}}}+....\infty \right]\]\[=\frac{1}{2}.{{\log }_{e}}\left( \frac{1+\frac{1}{2}}{1-\frac{1}{2}} \right)\] = \[\frac{1}{2}.{{\log }_{e}}\left( \frac{3/2}{1/2} \right)=\frac{1}{2}.{{\log }_{e}}(3)={{\log }_{e}}\sqrt{3}\].
You need to login to perform this action.
You will be redirected in
3 sec
