A) \[\frac{9}{32}\]
B) \[\frac{7}{16}\]
C) \[\frac{5}{16}\]
D) \[\frac{1}{210}\]
Correct Answer: C
Solution :
\[\frac{1}{1\times 4}+\frac{1}{4\times 7}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16}\] \[=\left( 1+\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{74}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16} \right)\times \frac{1}{3}=\frac{15}{16}\times \frac{1}{3}=\frac{5}{16}\]
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