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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)

best_answer

Here the greatest coefficient is { }^{2 n} C_n \therefore{ }^{2 n} C_n x^n>{ }^{2 n} C_{n+1} x^{n-1} \Rightarrow x>\frac{n}{n+1}

and { }^{2 n} C_n x^n>{ }^{2 n} 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)

Posted by

Shailly goel

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