Q. $\log_{e}3 - \frac{\log_{e}9}{2^{2}} + \frac{\log_{e}27}{3^{2}} - \frac{\log_{e}81}{4^{2}} + ...$ is
A) $\left( \log_{e}3 \right)(\log_{e}2)$
B) $\log_{e}3$
C) $\log_{e}2$
D) $\frac{\log_{e}5}{\log_{e}3}$
Explanation
(a)
$\log_{e}3 - \frac{\log_{e}9}{2^{2}} + \frac{\log_{e}27}{3^{2}} - \frac{\log_{e}81}{4^{2}} + ...$
$= \left( \log_{e}3 \right)\left( 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4}... \right)$
$= \left( \log_{e}3 \right)\log_{e}2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.