Question

$(\frac{1}{1\times 4}+\frac{1}{4\times 7}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16})$ is equal to

• A. $\frac{1}{3}$
• B. $\frac{5}{16}$
• C. $\frac{3}{8}$
• D. $\frac{41}{7280}$

Answer 1

The correct option is B $\frac{5}{16}$

$\frac{1}{1\times 4}+\frac{1}{4\times 7}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$

$=\frac{1}{3}[(1-\frac{1}{4})+(\frac{1}{4}-\frac{1}{7})+(\frac{1}{7}-\frac{1}{10})+(\frac{1}{10}-\frac{1}{13})+(\frac{1}{13}-\frac{1}{16})]$

$=\frac{1}{3}(1-\frac{1}{16})=\frac{1}{3}\times \frac{15}{16}=\frac{5}{16}$