If A and B denote the coefficients of  xn in the binomial expansions of (1+x)2n and (1+x)2n−1respectively, then

We have ,A = Coefficient of xn in (1+x)2n⇒A=2nCn⇒A=2nn2n−1Cn−1=22n−1Cn−1∵nCr=nrn−1Cr−1and , B = Coefficient of  xn in  (1+x)2n−1⇒B=2n−1Cn=2n−1Cn−1                  ∵nr=nCn−rClearly,  A = 2B.