" 8.If "n" is a positive integer,"sum_(r=0)^(n)C_(n)^(n)=

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

sum_(r=0)^(m)( n+r )C_(n)=

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)

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, 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

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)) )

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