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