If the coefficients of a^r-1, a^r and a^...

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.

Verified by Experts

The correct Answer is:

`n^2 - n (4r + 1) + 4r^2 - 2 = 0`

Similar Questions

Explore conceptually related problems

If the coefficients of r^(th) and (r+1)^(th) term in the expansion of (1+x)^(n) are equal then n=

If the coefficients of (r-5)^(th) and (2r - 1)^(th) terms in the expansion of (1 + x)^34 are equal, find r.

The coeffcients of the (r-1)^th , r^th and (r+1)^th terms in the expansion of (x+1)^n are in the ration 1 : 3: 5 Find n and r.

If the coefficient of the r^(th) term and the (r+1)^ (th) term is the expansion of (1+x)^(20) are in the ratio 1: 2 then r =

If the coefficients of r^(th) , (r+1)^(t h) and (r+2)^(th ) terms in the expansion of (1+x)^(14) are in A.P, then the value of r is

The coefficients of (2 r+4)^(th) and (r-2)^(th) terms in the expansion of (1+x)^(18) are equal. Then the value of r=

If r^(th) and (r+1)^(th) term in the expansion of (1+x)^(n) are equal, then n =

If the coefficient of rth, (r+1)th and (r+2)th terms in the binomial expansion of (1+y)^(m) are in A.P. then m and r satisfy the equation:

If x^(r ) occurs in the expansions of (x+(1)/(x))^(n) then its coefficient is

If x^(r) occurs in the expansion of (x+(1)/(x))^(n) , then is coefficient is