Home
Class 11
MATHS
If in the expansion of (1-x)^(2n-1), the...

If in the expansion of `(1-x)^(2n-1)`, the coefficient of `x^r` is denoted by `a_r`, then show that `a_(r-1)+a_(2n-r)=0`.

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    MODERN PUBLICATION|Exercise EXERCISE|221 Videos
  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

Similar Questions

Explore conceptually related problems

Show that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+ x)^(2n-1) .

Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+x)^(2n-1)

In the binomial expansion of (1+x)^34 , the coefficients of the (2r-1)th and the (r-5)th terms are equal. Find r.

If a_(0),a_(1),a_(2) ,…, a_(2n) are the coefficients in the expansion of (1 + x + x^(2))^(n) in ascending power of x show that a_(0)^(2) - a_(1)^(2) + a_(2)^(2) -…+ a_(2n)^(2) = a_(n) .

If t_r is the rth term is the expansion of (1 + a)^n , in ascending powers of a, prove that : r(r+1) t_(r+2)= (n-r+1)(n-r) a^2 t_r .

The coefficient of x^(50) in the series sum_(r=1)^(101)rx^(r-1)(1+x)^(101-r) is

If the coefficients of a^(r-1), a^(r ), a^(r+1) in the binomial expansion of (1 + a)^(n) are in Arithmetic Progression, prove that: n^(2) -n(4r+1) + 4r^(2) -2=0

Find the coefficient of x^(n-r) in the expansion of (x+1)^n (1+x)^n . Deduce that C_0C_r+C_1C_(r-1)+......+C_(n-r) C_n= ((2n!))/((n+r)!(n-r)!) .

Consider the binomial expansion of R = (1 + 2x )^(n) = I = f , where I is the integral part of R and f is the fractional part of R , n in N . Also , the sum of coefficient of R is 2187. If ith term is the greatest term for x= 1/3 , then i equal