A) \[\frac{1}{3}\]
B) \[\frac{5}{16}\]
C) \[\frac{3}{8}\]
D) \[\frac{41}{7280}\]
Correct Answer: B
Solution :
| [b] Given expression \[=\frac{1}{3}\left( 1-\frac{1}{4} \right)+\frac{1}{3}\left( \frac{1}{4}-\frac{1}{7} \right)+\frac{1}{3}\left( \frac{1}{7}-\frac{1}{10} \right)+\frac{1}{3}\left( \frac{1}{10}-\frac{1}{13} \right)\] \[+\frac{1}{3}\left( \frac{1}{13}-\frac{1}{16} \right)\] \[=\frac{1}{3}.\left\{ \begin{align} & 1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10} \\ & +\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16} \\ \end{align} \right\}\] \[=\frac{1}{3}\left( 1-\frac{1}{16} \right)=\left( \frac{1}{3}\times \frac{15}{16} \right)=\frac{5}{16}\] |
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