If A and B are the coefficient of

The coefficient of xn is (1 + x)2n is ?

Since Tr +1 = 2nCr xr

For xn coefficient put r = n

i.e coefficient of xn is 2nCn 

i.e. A = 2nCn

and for coefficient of xn in (1 + x)2n–1

Tr +1 = 2n–1Cr xr

Put r = n

i.e. coefficient of xn in (1 + x)2n–1 is 2n–1Cn

i.e B = 2n–1Cn

$\therefore \frac{A}{B}=\frac{{ }^{2 n} C_{n}}{{ }^{2 n-1} C_{n}}=\frac{(2 n) ! n ! n !}{n ! n !(2 n-1) !}$

= 2