(B) The coefficient of $x^n$ in the expansion of $(1 + x)^{2n}$ is $A = ^{2n}C_n$.The coefficient of $x^n$ in the expansion of $(1 + x)^{2n - 1}$ is $

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(B) The coefficient of $x^n$ in the expansion of $(1 + x)^{2n}$ is $A = ^{2n}C_n$.The coefficient of $x^n$ in the expansion of $(1 + x)^{2n - 1}$ is $B = ^{2n-1}C_n$.Taking the ratio $\frac{A}{B}$:$\frac{A}{B} = \frac{^{2n}C_n}{^{2n-1}C_n} = \frac{(2n)!}{n!n!} \times \frac{n!(n-1)!}{(2n-1)!}$$= \frac{(2n)(2n-1)!}{n(n-1)!n!} \times \frac{n!(n-1)!}{(2n-1)!}$$= \frac{2n}{n} = 2$Therefore,$A = 2B$.

Class 11 Mathematics Binomial Theorem General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

Medium

If $A$ and $B$ are the coefficients of $x^n$ in the expansions of $(1 + x)^{2n}$ and $(1 + x)^{2n - 1}$ respectively,then

A
$A = B$
B
$A = 2B$
C
$2A = B$
D
None of these

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