Q. The sum of the series $2\lbrack 7^{- 1} + 3^{- 1}.7^{- 3} + 5^{- 1}.7^{- 5} + ...\rbrack$ is
A) $\log_{e}\left( \frac{4}{3} \right)\$
B) $\log_{e}\left( \frac{3}{4} \right)$
C) $2\log_{e}\left( \frac{3}{4} \right)$
D) $2\log_{e}\left( \frac{4}{3} \right)$
Explanation
(a)
$2\left\lbrack \frac{1}{7} + \frac{1}{3}.\frac{1}{7^{3}} + \frac{1}{5}.\frac{1}{7^{5}} + ... \right\rbrack = \log_{e}\left\lbrack \frac{1 + \frac{1}{7}}{1 - \frac{1}{7}} \right\rbrack = \log_{e}\frac{4}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.