Q. The sum of series $\frac{1}{1.2} - \frac{1}{2.3} + \frac{1}{3.4} - \ldots\infty$ is equal to
A) $2\log_{e}2$
B) $\log_{e}{2 - 1}$
C) $\log_{e}2$
D) $\log_{e}\left( \frac{4}{e} \right)$
Explanation
(d)
$\frac{1}{1.2} - \frac{1}{2.3} + \frac{1}{3.4} - ... = \left( 1 - \frac{1}{2} \right) - \left( \frac{1}{2} - \frac{1}{3} \right) + \left( \frac{1}{3} - \frac{1}{4} \right) - \ \ldots$
$= 2\left( 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \ldots \right) - 1 = \log_{e}\frac{4}{e}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.