A) \[\frac{2}{99}\]
B) \[\frac{1}{25}\]
C) \[\frac{1}{50}\]
D) \[\frac{1}{100}\]
Correct Answer: C
Solution :
Expression \[=\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)\left( 1-\frac{1}{5} \right).......\left( 1-\frac{1}{99} \right)\left( 1-\frac{1}{100} \right)\] \[=\left( \frac{3-1}{3} \right)\left( \frac{4-1}{4} \right)\left( \frac{5-1}{5} \right).......\left( \frac{99-1}{99} \right)\left( \frac{100-1}{100} \right)\] \[=\frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}\times ........\times \frac{98}{99}\times \frac{99}{100}\] \[=\frac{2}{100}=\frac{1}{50}\]
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