`underset(r=0)overset(10)sumr^(10)C_(r),3^(r).(-2)^(10-r)` is -

sum_(r=0)^(10) r.^(10)C_(r),3^(r).(-2)^(10-r) is -

underset(r=1)overset(n)(sum)r(.^(n)C_(r)-.^(n)C_(r-1)) is equal to

If (1-x^(3))^(n)=underset(r=0)overset(n)(sum)a_(r)x^(r)(1-x)^(3n-2r) , then the value of a_(r) , where n in N is

underset(r=0)overset(n)(sum)(-1)^(r).^(n)C_(r)[(1)/(2^(r))+(3^(r))/(2^(2r))+(7^(r))/(2^(3r))+(15^(r))/(2^(4r))+ . . .m" terms"]=

underset(r=0)overset(n-1)(sum)(.^(n)C_(r))/(.^(n)C_(r)+.^(n)C_(r+1)) equals

let underset(r=0)overset(2010)(sum)a_(r)x^(r)=(1+x+x^(2)+x^(3)+x^(4)+x^(5))^(402) and underset(r=0)overset(2010)(sum)a_(r)=a, then the value of ((underset(r=0)overset(2010)(sum)r.a_(r))/(underset(r=0)overset(2010)(sum)a_(r))) is equal to____.

Statement-1: In the expansion of (sqrt(5)+3^(1//5))^(10) , sum of integral terms is 3134. Statement-2: (x+y)^(n)=underset(r=0)overset(n)(sum).^(n)C_(r)*x^(n-r)y^(r) .

underset(r=1)overset(n)sum ( r )/(r^(4)+r^(2)+1) is equal to