[" 2.If "(1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+...+a_(2n)x^(2n)],[" then "a_(0)+a_(3)+a_(6)+------y=]

If n ge 2 , and (1 + x + x^(2))^(n) = a_(0) + a_(1)x + a_(2)x^(2) + .. . +a_(2n) x^(2n) , then a_(0) - 2a_(1)+ 3a_(2) + ... + (2n + 1)a_(n) = ______

If (1 +x + x^(2))^(n) = a_(0) + a_(1) x + a_(2) x^(2) + … + a_(2n) x^(2n) , then a_(0) + a_(2) + a_(4) + … + a_(2n) equals

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+...+a_(2n)x^(2n), then a_(0)+a_(2)+a_(4)+....+a_(2n) is

( 1 + x + x^(2))^(n) = a_(0) + a_(1) x + a_(2) x^(2) + …+ a_(2n) x^(2n) , then a_(0) + a_(1) + a_(2) + a_(3) - a_(4) + … a_(2n) = .

(1+x)^(n)=a_(0)+a_(1)x+a_(2)*x^(2)+......+a_(n)x^(n) then prove that

If (1 + x)^(2n) = a_(0) + a_(1) x + a_(2) x^(2) +… + a_(2n) x^(2n) , then (a_(0) - a_(2) + a_(4) - a_(6) +…- a_(2n))^(2)+(a_(1) - a_(3) + a_(5) - a_(7) +...+a_(2n-1))^(2) is equal to

If (1+x+x^(2))^(n) = a_(0)+a_(1) x+a_(2) x^(2)+.. .+a_(2 n) x^(2 n) then the value of a_(0)+a_(3)+a_(6)+.. . . is

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then prove that a_(0)+a_(3)+a_(6)+a_(9)+……=3^(n-1)