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