If n is even positive integer, then the condi | vedclass

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Question

(a) If $n$ is even, the greatest coefficient is $^n{C_{n/2}}$

Therefore the greatest term $ = {\,^n}{C_{n/2}}{x^{n/2}}$

$	herefore \,{\,^n}{C_{

Vedclass · Accepted Answer

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

Vedclass · Answer

(a) If $n$ is even, the greatest coefficient is $^n{C_{n/2}}$ Therefore the greatest term $ = {\,^n}{C_{n/2}}{x^{n/2}}$ $ herefore \,{\,^n}{C_{n/2}}{x^{n/2}} > {\,^n}{C_{(n/2) - 1}}{x^{(n - 2)/2}}$ and $^n{C_{n/2}}{x^{n/2}} > {\,^n}{C_{(n/2) + 1}}{x^{(n/2) + 1}}$ ==> $\frac{{n - \frac{n}{2} + 1}}{{\frac{n}{2}}}x > 1$and $\frac{{\frac{n}{2}}}{{\frac{n}{2} + 1}}x < 1$ ==> $x > \frac{{\frac{n}{2}}}{{\frac{n}{2} + 1}}$ and $x < \frac{{\frac{n}{2} + 1}}{{\frac{n}{2}}}$ ==> $x > \frac{n}{{n + 2}}$and $x < \frac{{n + 2}}{n}$

If $n$ is even positive integer, then the condition that the greatest term in the expansion of ${(1 + x)^n}$ may have the greatest coefficient also, is

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