Q. The sum of the series $\frac{1}{3 \times 7} + \frac{1}{7 \times 11} + \frac{1}{11 \times 15} + ...$ is
A) $\frac{1}{3}$
B) $\frac{1}{6}$
C) $\frac{1}{9}$
D) $\frac{1}{12}$
Explanation
(d)
Let $S = \frac{1}{3 \times 7} + \frac{1}{7 \times 11} + \frac{1}{11 \times 15} + ...\infty$
$= \frac{1}{4}\left\lbrack \left\{ \frac{1}{3} - \frac{1}{7} \right\} + \left\{ \frac{1}{7} - \frac{1}{11} \right\} + ... \right\rbrack\ \$
$= \frac{1}{4}\left\lbrack \frac{1}{3} + 0 \right\rbrack = \frac{1}{12}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.