If (1+x)^n=C0+C1x+C2x^2+……..+Cnx^n then ...

If `(1+x)^n=C_0+C_1x+C_2x^2+……..+C_nx^n` then the value of `sumsum_(0lt=iltjlt=n)C_iC_j` is
(A) `2^(2n-1)- .^(2n)C_(n/2)`
(B) `.^(2n)C_n`
(C) `2^n`
(D) none of these

AI Generated Solution

Similar Questions

Explore conceptually related problems

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) , then the value of sumsum_(0lerltslen)(C_(r)+C_(s))^(2) is :

(1+x)=C_(0)+C_(1)x+….+C_(n)x^(n) then the value of sumsum_(0lerltslen)C_(r)C_(s) is equal to :

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) , then the value of sumsum_(0lerltslen)(r+s)(C_(r)+C_(s)) is :

If (1+x)^n=C_(0)+C_(1)x+C_(2)x^2+….+C_(n)x^n then prove that (SigmaSigma)_(0 le i lt j le n ) C_(i)C_(j)^2=(n-1)^(2n)C_(n)+2^(2n)

If (1+x)^n=c_0+c_1x+c_2x^2+...+c_nx^n then the value of c_0+3c_1+5c_2+....+(2n+1)c_n is-

If (1+x)^n=C_0+C_1x+C_2x^2+...+C_nx^n then the value of (C_0)^2+(C_1)^2/2+(C_2)^2/3+...+(C_n)^2/(n+1) is equal to

If (1+x)^n = C_0 + C_1x + C_2x^2 + ……..+C_n.x^n then find C_0 - C_2 + C_4 - C_6 + …….

If (1 + x)^(n) = C_(0) = C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , find the values of the following (sumsum)_(0leilt j le n)jC_(i)

If (1 + x)^(n) = C_(0) = C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , find the values of the following (sumsum)_(0leile jlen)(i +j)(C_(i)pmC_(j) )^(2)

If (1+x)^n=C_0+C_1x+C_2x^2=……..+C_nx^n show that sum_(r=0)^(n-3) C_r C_(r+3) = ((2n)!)/((n+3)!(n-3)!)