[" 15) If "a_(x)" is the coefficient of "x^(r)," in the expansion "],[" of "(1+x+x^(2))^(n)," then "a_(1)-2a_(2)+3a_(3)-...-2na_(2n)=],[[" A) "2n," B) "-n],[" C) "n," D) "0]]

If a_(r) is the coefficient of x^(r) in the expansion of (1+x+x^(2))^(n), then a_(1)-2a_(2)+3a_(3)....-2na_(2n)=

If a_(k) is the coefficient of x^(k) in the expansion of (1+x+x^(2))^(n) for k=0,1,2,......,2n then a_(1)+2a_(2)+3a_(3)+...+2na_(2n)=

If a _(r) is the coefficient of x^r in the expansion of (1+ x+x^(2)) ^(n), then the value of a_(1)- 2a_(2) +3a_(3)-4a_(4)+…-2na_(2n) is -

If a_(r) be the coefficient of x^(r) in the expression of (1+bx^(2)+cx^(3))^(n), then prove that,2na_(4)=(n-1)a_(2)^(2)

If a_(r) be the coefficient of x^(r) in the expression (1+bx^(2)+cx^(3))^(n)" ,Prove that " 2na_(4)=(n-1)a_(2)^(2)

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

If a_(r) is the coefficient of x^(r) in (1-2x+3x^(2))^(n), then sum_(r=0)^(2n)r*a_(r)=

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

If a_(0), a_(1), a_(2),… are the coefficients in the expansion of (1 + x + x^(2))^(n) in ascending powers of x, prove that a_(0) a_(2) - a_(1) a_(3) + a_(2) a_(4) - …+ a_(2n-2) a_(2n)= a_(n+1) .