Greatest coefficient in expansion of {(1 + x)^{2n + 2}} is

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7.Binomial Theorem

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The greatest coefficient in the expansion of ${(1 + x)^{2n + 2}}$ is

A

$\frac{{(2n)!}}{{{{(n!)}^2}}}$

B

$\frac{{(2n + 2)!}}{{{{\{ (n + 1)!\} }^2}}}$

C

$\frac{{(2n + 2)!}}{{n!(n + 1)!}}$

D

$\frac{{(2n)!}}{{n!(n + 1)!}}$

Solution

(b) Greatest coefficient of ${(1 + x)^{2n + 2}}$ is
$ = {\,^{(2n + 2)}}{C_{n + 1}} = \frac{{(2n + 2)!}}{{{{\{ (n + 1)!\} }^2}}}$

Standard 11

Mathematics

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