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The interval in which x must lie so that the greatest term in the expansion of (1+x)^{2 n} has the greatest coefficient is

Option: 1

\left(\frac{n-1}{n}, \frac{n}{n-1}\right)


Option: 2

\left(\frac{n}{n+1}, \frac{n+1}{n}\right)


Option: 3

\left(\frac{n}{n+2}, \frac{n+2}{n}\right)


Option: 4

None of these


Answers (1)

Here the greatest coefficient is { }^{2 n} C_n \therefore \quad{ }^{2 n} C_n x^n>{ }^{2 n} C_{n+1} x^{n-1} \Rightarrow x>\frac{n}{n+1} \text { and }{ }^{2 n} C_n x^n>{ }^{2 n} C_{n-1} x^{n+1} \Rightarrow x<\frac{n+1}{n} Hence the result is (b)

 

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Ramraj Saini

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