If n is even and the value of ^nC_r is maximu | vedclass

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Question

(A) The binomial coefficient series is given by $^nC_0, ^nC_1, ^nC_2, \ldots, ^nC_r, \ldots, ^nC_{n-1}, ^nC_n$.The value of the binomial coefficients

Vedclass · Accepted Answer

$\frac{n}{2}$

Vedclass · Answer

(A) The binomial coefficient series is given by $^nC_0, ^nC_1, ^nC_2, \ldots, ^nC_r, \ldots, ^nC_{n-1}, ^nC_n$.The value of the binomial coefficients increases initially,reaches a maximum,and then decreases.For a given $n$,the total number of terms in the expansion is $n+1$.If $n$ is even,the total number of terms $n+1$ is odd,so there is a single middle term.The position of the middle term is given by $\frac{(n+1)+1}{2} = \frac{n}{2} + 1$.Since $^nC_r$ represents the $(r+1)$-th term,we set $r+1 = \frac{n}{2} + 1$,which gives $r = \frac{n}{2}$.Thus,when $n$ is even,the maximum value of $^nC_r$ occurs at $r = \frac{n}{2}$.

If $n$ is even and the value of $^nC_r$ is maximum,then $r = $

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