A) \[\left( \frac{n-1}{n},\frac{n}{n-1} \right)\]
B) \[\left( \frac{n}{n+1},\frac{n+1}{n} \right)\]
C) \[\left( \frac{n}{n+2},\frac{n+2}{n} \right)\]
D) None of these
Correct Answer: B
Solution :
Here the greatest coefficient is \[^{2n}{{C}_{n}}\] \[\therefore \,\,{{\,}^{2n}}{{C}_{n}}{{x}^{n}}{{>}^{2n}}{{C}_{n+1}}{{x}^{n-1}}\Rightarrow x>\frac{n}{n+1}\] and \[^{2n}{{C}_{n}}{{x}^{n}}>{{\,}^{2n}}{{C}_{n-1}}{{x}^{n+1}}\Rightarrow x<\frac{n+1}{n}\] Hence the required interval is \[\left( \frac{n}{n+1},\,\frac{n+1}{n} \right)\].
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