Question

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. $\frac{1}{12}$

Answer 1

Answer: (D)

$\frac{1}{12}$

$\frac{1}{3\times 7}+\frac{1}{7\times 11}+\frac{1}{11\times 15}+....$

$\frac{1}{4}(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...)$

$\frac{1}{4}\times \frac{1}{3}=\frac{1}{12}$