If n is a positive integer, `sum_(r=0)^n (^n C_r)^2=`

If n is a positive integer,then sum_(r=1)^(n)r^(2)*C_(r)=

If n is a positive integer,then sum_(r=2)^(n)r(r-1)*C_(r) =

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)

Assertion: If n is an even positive integer n then sum_(r=0)^n ("^nC_r)/(r+1) = (2^(n+1)-1)/(n+1) , Reason : sum_(r=0)^n ("^nC_r)/(r+1) x^r = ((1+x)^(n+1)-1)/(n+1) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: If n is an even positive integer n then sum_(r=0)^n ^nC_r/(r+1) = (2^(n+1)-1)/(n+1) , Reason : sum_(r=0)^n ^nC_r/(r+1) x^r = ((1+x)^(n+1)-1)/(n+1) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

If n is a positive integer and C_(r )= ""^(n)C_(r ) then find the vlaue of sum_(r =1)^(n) r^(2)((C_(r ))/(C_(r -1))) .

If n is a positive integer and C_r = ""^nC_r then find the value of sum_(x = 1)^n r^2 ((C_r)/(C_(r - 1)) )

If n is a positive integer, for (1+x)^(n) ,then sum_(r=0)^(n).^nC_(r)=

If n is a positive integer and C_4 = ""^nC_r then find the value of sum_(x = 1)^n r^2 ((C_r)/(C_(r - 1)) )

If n is a positive integer and if (1+x+x^(2))^(2n)=underset(r=0)overset(2n)(sum)a_(r)x^(r) , then