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