Question

If the coefficients of a^(r-1),a^r and a^(r+1) in the expansion of (1+a)^n are in arithmetic progression, prove that n^2 - n(4r+1) +4r^2 - 2=0

Answer 1

Answer:

nCr-1,nCr,nCr+1 are in ap

a1=nCr-1=n!÷(n-r+1)!(r+1)!.

a2=nCr=n!÷(n-r)!(r)!

a3=nCr+1=n!÷(n-r-1)!(r+1)!

now apply a2-a1=a3-a2