If `sum_(r=1)^n r^3((C(n,r))/(C(n,r-1)))=14^2` then `n=`

Prove that sum_(r = 1)^n r^3 ((n_C_r)/(C_(r - 1)))^2 = (n (n + 1)^2 (n+2))/(12)

Prove that sum_(r = 1)^n r^3 ((C_r)/(C_(r - 1))^2) = (n (n + 1)^2 (n+2))/(12)

If C_(r) stands for ""^(n)C_(r) and sum_(r=1)^(n)(r*C_(r))/(C_(r-1))=210 , then n equals:

If sum_(r=0r=0)^(n){(C(n,r-1))/(C(n,r)+C(n,r-1))}^(3)=(25)/(24)

If n is a positive integer, prove that sum_(r=1)^(n)r^(3)((""^(n)C_(r))/(""^(n)C_(r-1)))^(2)=((n)(n+1)^(2)(n+2))/(12)

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

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

sum_(r=1)^(n)(C(n,r))/(r+2) is equal to

sum_(r=1)^(n)r(r+1)=((n+a)(n+b)(n+c))/(3) then