A) \[\frac{1}{2n}\]
B) \[\frac{1}{5n}\]
C) \[\frac{1}{3n}\]
D) \[\frac{1}{n}\]
Correct Answer: D
Solution :
Given expression \[=\left( 1-\frac{1}{2} \right)\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)...\left( 1-\frac{1}{n-1} \right)\left( 1-\frac{1}{n} \right)\] \[=\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}\times ...\times \frac{n-2}{n-1}\times \frac{n-1}{n}=\frac{1}{n}\]
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