If `(2x^2+3x+4)^(10)=sum_(r=0)^(20) a_r x^r`, then `(a_7)/(a_(13)`=

If (1-x-x^(2))^(20)=sum_(r=0)^(40)a_(r).x^(r), then

If (1-x-x^(2))^(20)=sum_(r=0)^(40)a_(r)x^(r), then a_(1)+3a_(3)+5a_(5)+.......+39a_(39)=

If (1+x-2x^(2))^(6)=sum_(r=0)^(12)a_(r).x^(r) then a_(1)+a_(3)+......a_(11)

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

(1+x-2x^(2))^(6)=sum_(r=0)^(12)a_(r)x^(r) then a_(2)+a_(4)+....+a_(12)=

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

If (1+2x+x^(2))^(n)=sum_(r=0)^(2n)a_(r)x^(r), then a=(^(n)C_(2))^(2) b.^(n)C_(r).^(n)C_(r+1) c.^(2n)C_(r) d.^(2n)C_(r+1)