# Prove that the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient of xn in the expansion of (1 + x)2n – 1.

The general term Tr+1 in the binomial expansion is given by Tr+1 = nCr an-r br

The general term for binomial (1+x)2n is

Tr+1 = 2nCr xr …………………..1

To find the coefficient of xn

r=n

Tn+1 = 2nCn xn

The coefficient of xn = 2nCn

The general term for binomial (1+x)2n-1 is

Tr+1 = 2n-1Cr xr

To find the coefficient of xn

Putting n =r

Tr+1 = 2n-1Cr xn

The coefficient of xn = 2n-1Cn

We have to prove

Coefficient of xn in (1+x)2n = 2 coefficient of xn in (1+x)2n-1

Hence L.H.S = R.H.S.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Greatest term in binomial expansion | Revising Binomial theorem43 mins
Finding remainder using binomial theorem43 mins
Quiz on Greatest term in binomial expansion | Revising Binomial theorem38 mins
Binomial theorem for any index | Interactive Quiz48 mins
Finding coefficient of x^n in binomial expansion59 mins
Lecture on properties of Binomial Coefficients58 mins
Interactive Quiz on properties of Binomial Coefficients51 mins
Master on Binomial Theorem for any index41 mins
Interactive Quiz on Binomial Theorem40 mins
Interactive Quiz | general & middle terms53 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses