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

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

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

The value sum_(r=1)^(10)r.(n_(C_(r)))/(n_(C_(r-1))) is equal to

Find the sum sum_(r=1)^(n)r^(2)(^nC_(r))/(n_(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 sum_(r=0)^(2n)(-1)^(r)(2n(C_(r))^(2)=alpha_(1), then sum_(r=0)^(2n)(-1)^(r)(r-2n)(2n(C_(r))^(2)=