# If $A$ and $B$ are coefficient of $x^n$ in the expansion of $(1+x)^{2n}$ and $(1+x)^{2n-1}$ respectively then $A/B$ equals

$\begin{array}{1 1}(A)\;1\\(B)\;2\\(C)\;\large\frac{1}{2}\\(D)\;\large\frac{1}{n}\end{array}$

Toolbox:
• $T_{r+1}=nC_r a^{n-r}b^r$
$(1+x)^{2n}$
$T_{r+1}=2nC_r (1)^{n-r}x^r$
$(1+x)^{2n-1}=2n-1C_r(1)^{2n-1-r}x^r$
The coefficient of $x^n$
$\Rightarrow 2nC_n$ & $2n-1C_n$
$\large\frac{A}{B}=\frac{2nC_n}{2n-1C_n}$
$\Rightarrow 2$
Hence (B) is the correct answer.