Let `n in N`. If `(1+x)^(n)=a_(0)+a_(1)x+a_(2)x^(2)+…….+a_(n)x^(n)` and `a_(n)-3,a_(n-2), a_(n-1)` are in AP, then :

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

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) where a_(0) , a(1) , a(2) are unequal and in A.P., then (1)/(a_(n)) is equal to :

Let (1 + x^(2))^(2) (1 + x)^(n) = a_(0) + a_(1) x + a_(2) x^(2) + … if a_(1),a_(2) " and " a_(3) are in A.P , the value of n is

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

Let n be a positive integer and (1+x)^(n)=a_(0)+a_(1)x+a_(2)x^(2)+…..+a_(n)x^(n)" What is "a_(0)+a_(1)+a_(2)+….+a_(n) equal to ?

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)++a_(2n)x^(2n) find the value of a_(0)+a_(3)+a_(6)++,n in N

If (1-x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)++a_(2n)x^(2n) find the value of a_(0)+a_(2)+a_(4)++a_(2n)

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) = ______