In the expansion of `(1 + x)^(n) (1 + y)^(n) (1 + z)^(n)` , the sum of the co-efficients of the terms of degree 'r' is (a) `.^(n^3)C_r` (b) `.^nC_(r^3)` (c) `.^(3n)C_r` (d) `3.^(2n)C_r`

Prove that in the expansion of (1+x)^n(1+y)^n(1+z)^n , the sum of the coefficients of the terms of degree ri s^(3n)C_r .

Prove that .^(n)C_(r )+.^(n-1)C_(r )+..+.^(r )C_(r )=.^(n+1)C_(r+1)

Statement-1: If underset(r=1)overset(n)(sum)r^(3)((.^(n)C_(r))/(.^(n)C_(r-1)))^(2)=196 , then the sum of the coeficients of powerr of xin the expansion of the polynomial (x-3x^(2)+x^(3))^(n) is -1. Statement-2: (.^(n)C_(r))/(.^(n)C_(r-1))=(n-r+1)/(r) AA n in N and r in W .

If C_(0), C_(1), C_(2), …, C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then sum_(r=0)^(n)sum_(s=0)^(n)C_(r)C_(s) =

If sum_(r=1)^(n) r(r+1) = ((n+a)(n+b)(n+c))/(3) , where a gt b gt c , then

If C_(0), C_(1), C_(2),…, C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then sum_(r=0)^(n)sum_(s=0)^(n)(C_(r) +C_(s))

Show that: .^nC_(n-r)+3.^nC_(n-r+1)+3.^nC_(n-r+2)+^nC_(n-r+3)=^(n+3)C_r .

Find the sum sum_(r=1)^(n) r^(2) (""^(n)C_(r))/(""^(n)C_(r-1)) .

The expression ""^(n)C_(r)+4.""^(n)C_(r-1)+6.""^(n)C_(r-2)+4.""^(n)C_(r-3)+""^(n)C_(r-4)

The value of sum_(r=0)^(3n-1)(-1)^r ^(6n)C_(2r+1)3^r is