If `p+q=1,` then show that `sum_(r=0)^n r^2^n C_rp^r q^(n-r)=n p q+n^2p^2dot`

If p+q=1, then show that sum_(r=0)^nr^2^nC_rp^rq^(n-r)=npq+n^2p^2

If p+q=1, then show that sum_(r=0)^(n)r^(n)C_(r)p^(r)q^(n-r)=npq+n^(2)p^(2)

If p+q=1 then show that sum_(r=0)^(n)r^(2)C_(r)p^(r)q^(n-r)=npq+n^(2)p^(2)

Prove that sum_(r=0)^n r(n-r)(^nC_ r)^2=n^2(^(2n-2)C_n)dot

If p+q=1, then value of sum_(r=0)^(n)r^(2)C(n,r)p^(r)q^(n-r) is (1)npq(2)np(1+q) (3) n^(2)p^(2)+npq(4)np^(2)+npq

Prove that sum_(r=0)^n r(n-r)(.^nC_ r)^2=n^2(.^(2n-2)C_n)dot

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) = .

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) = .

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

If p, q, r, s are in G.P, show that (p^n + q^n) , (q^n + r^n) , (r^n + s^n) are also in G.P