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

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

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

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.

Consider (1 + x + x^(2))^(n) = sum_(r=0)^(n) a_(r) x^(r) , where a_(0), a_(1), a_(2),…, a_(2n) are real number and n is positive integer. The value of sum_(r=0)^(n-1) a_(r) is

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

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

Let n be a positive integer and (1+x)^(n)+C_(0)+C_(1)x+C_(2)x^(2)+C_(3)x^(3)+ . . .+C_(r)x^(r)+ . . .+C_(n-1)x^(n-1)+C_(n)x^(n) Where C_(r) stands for .^(n)C_(r) , then Q. The value of underset(r=0)overset(n)(sum)underset(s=0)overset(n)(sum),C_(r),C_(S) is