[" ILLUSTRATION "20" 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 C_(0), C_(1), C_(2),…, C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then sum_(r=0)^(n)(r+1)(C_(r))

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

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

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

If C_(o)C_(1),C_(2),......,C_(n) denote the binomial coefficients in the expansion of (1+x)^(n), then the value of sum_(r=0)^(n)(r+1)C_(r) is

If C_0,C_1,C_2,.......,C_n denote the binomial coefficients in the expansion of (1+1)^n, then sum_(0ler) sum_(< s le n) (C_r+C_s)

If C_o C_1, C_2,.......,C_n denote the binomial coefficients in the expansion of (1 + x)^n , then the value of sum_(r=0)^n (r + 1) C_r is

If C_(0),C_(1),C_(2)..C_(n) denote the coefficients in the binomial expansion of (1+x)^(n), then C_(0)+2.C_(1)+3.C_(2)+.(n+1)C_(n)

If ""(n)C_(0), ""(n)C_(1), ""(n)C_(2), ...., ""(n)C_(n), denote the binomial coefficients in the expansion of (1 + x)^(n) and p + q =1 sum_(r=0)^(n) r^(2 " "^n)C_(r) p^(r) q^(n-r) = .