Home
Class 11
MATHS
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.

Text Solution

Verified by Experts

The correct Answer is:
`n^2 - n (4r + 1) + 4r^2 - 2 = 0`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    NCERT BANGLISH|Exercise EXERCISE 8.1|14 Videos

  • BINOMIAL THEOREM

    NCERT BANGLISH|Exercise EXERCISE 8.2|12 Videos

  • APPENDIX 2 MATHEMATICAL MODELLING

    NCERT BANGLISH|Exercise EXAMPLE|2 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISES ON CHAPTER 24|1 Videos

Similar Questions

Explore conceptually related problems

In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binomial expansion of (1+y)^m are in A.P., then prove that m^2-m(4r+1)+4r^2-2=0.

Find the coefficients of y^(2r+1) in the expansion of (y-(1)/(y))^(2n+1)

If the coefficient of x^(r)andx^(r+1) are equal in the expansion of (1+x)^(2n+1) , then find the value of r .

Prove that the coefficient of x^r in the expansion of (1-2x)^(-1/2) is (2r!)/[(2^r)(r!)^2]

prove that the coefficient of the (r +1)th term in the expansion of (1+x)^(n) is equal to the sum of the coefficients of the rth and (r+1)th terms in the expansion of (1+x)^(n-1)

If a _(r) is the coefficient of x^r in the expansion of (1+ x+x^(2)) ^(n), then the value of a_(1)- 2a_(2) +3a_(3)-4a_(4)+…-2na_(2n) is -

If a_(r) be the coefficient of x^(r) in the expression of (1+bx^(2)+cx^(3))^(n),"then prove that" , a_(3)=nc

If r gt 1, n gt2 are positive integers and the coefficients of (r+2) th and 3rd terms in the expansion of (1+x)^(2n) are equal, then n is equal to-

Show that the sum of the coefficient of first (r+1) terms in the expansions of (1-x)^(-n) is ((n+1)(n+2)...(n+r))/(r!)

If r^[th] and (r+1)^[th] term in the expansion of (p+q)^n are equal, then [(n+1)q]/[r(p+q)] is (a) 1/2 (b) 1/4 (c) 1 (d) 0