A) 156
B) 162
C) 165
D) 126
Correct Answer: A
Solution :
(a): \[1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}=\frac{a}{b}\] \[\frac{a}{b}=\left( 1-\frac{1}{13} \right)=\frac{12}{13}\] \[\therefore a\times b=12\times 13=156\]
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