n ಧನಾತ್ಮಕ ಪೂರ್ಣಾಂಕವಾಗಿದ್ದರೆ ಮತ್ತು if(1+x+x^(2))^(2n)=underset(r=0)overset(2n)(sum)a_(r)x^(r), ನಂತರ .. .

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

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 (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

If (1+x+x^(2))^(n)=sum_(r=0)^(2n)a_(r)x^(r), then prove that a_(r)=a_(2n-r)

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

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) .

If (1+x+x^(2))^(n)=sum_(r=0)^(2n)a_(r)x^(r), then a_(1)-2a_(2)+3a_(3)-...-2na_(2n)=

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____.