[" If "a_(r)" is the coefficient "x^(r)" in the "],[" expansion of "(1+x+x^(2))^(n)" 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 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_(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) be the coefficient of x^(r) in the expression of (1+bx^(2)+cx^(3))^(n),"then prove that" , a_(3)=nc

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 a_(r) is the coefficient of x^(r ) in the expansion of (1+x+x^(2))^(n)(n in N) . Then the value of (a_(1)+4a_(4)+7a_(7)+10a_(10)+……..) is equal to :

If a_(r) is the coefficient of x^(r ) in the expansion of (1+x+x^(2))^(n)(n in N) . Then the value of (a_(1)+4a_(4)+7a_(7)+10a_(10)+……..) is equal to :

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