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  • In n is an even positive integer, then the condition that the greatest term in the expansi

In n is an even positive integer, then the condition that the greatest term in the expansion of (1+x)^n  many have the greatest coefficient also, is ( x is positive)

Option: 1

\frac{n}{n+2} < x < \frac{n+2}{n}


Option: 2

\frac{n+1}{n} < x < \frac{n }{n+1}


Option: 3

\frac{n}{n+4} < x < \frac{n+4}{4}


Option: 4

none of these 


Answers (1)

best_answer

Let n = 2m

If n is even then greatest binomial coefficient = ^n C_{n/2} = ^{2m}C_m 

                                                                            = (m+1) th term = T_{m+1}

Now, since T_{m+1}  is greatest term

                         m < \frac{(2m+1)}{1+\left | \frac{1}{x} \right | < (m+1)

Solving it and putting m = n/2 we get 

\frac{n}{n+2} < x < \frac{n+2}{n}

 

 

Posted by

Ritika Kankaria

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