[(1)/(1-2x+x^(2))=1+bx+b_(2)x^(2)+b_(1)x^(3)+...x_(0)|x|<1],[" then the value of "b_(1)" is "]

If quad 1(1)/(1-2x+x^(2))=1+b_(1)x+b_(2)x^(2)+b_(3)x^(3)+...oo,|x|<1, then the value of b_(1) is

If |(1 +ax,1 +bx,1 + bx),(1 +a_(1) x,1 +b_(1) x,1 + c_(1) x),(1 + a_(2) x,1 + b_(2) x,1 + c_(2) x)| = A_(0) + A_(1) x + A_(2) x^(2) + A_(3) x^(3) , then A_(1) is equal to

If |(1 +ax,1 +bx,1 + bx),(1 +a_(1) x,1 +b_(1) x,1 + c_(1) x),(1 + a_(2) x,1 + b_(2) x,1 + c_(2) x)| = A_(0) + A_(1) x + A_(2) x^(2) + A_(3) x^(3) , then A_(1) is equal to

Find the coefficient of x in the determinant |((1+x)^(a_1 b_1),(1+x)^(a_1 b_2),(1+x)^(a_1 b_3)),((1+x)^(a_2 b_2),(1+x)^(a_2 b_2),(1+x)^(a_2 b_3)),((1+x)^(a_3 b_3),(1+x)^(a_3 b_2),(1+x)^(a_3 b_3))|=0.

Find the coefficient of x in the determinant |{:((1+x)^(a_(1)b_(1)),(1+x)^(a_(1)b_(2)),(1+x)^(a_(1)b_(3))),((1+x)^(a_(2)b_(1)),(1+x)^(a_(2)b_(2)),(1+x)^(a_(2)b_(3))),((1+x)^(a_(3)b_(1)),(1+x)^(a_(3)b_(2)),(1+x)^(a_(3)b_(3))):}|

Find the coefficient of x in the determinant |{:((1+x)^(a_(1)b_(1)),(1+x)^(a_(1)b_(2)),(1+x)^(a_(1)b_(3))),((1+x)^(a_(2)b_(1)),(1+x)^(a_(2)b_(2)),(1+x)^(a_(2)b_(3))),((1+x)^(a_(3)b_(1)),(1+x)^(a_(3)b_(2)),(1+x)^(a_(3)b_(3))):}|

Let for a!=a_(1)!=0,f(x)=ax^(2)+bx+cg(x)=a_(1)x^(2)+b_(1)x+c_(1) and p(x)=f(x)-g(x). If p(x)=0 only for x=-1 and p(-2)=2 then the value of p(2)

If z=|(1+ax,1+bx,1+cx),(1+a_(1)x,1+b_(1)x,1+c_(1)x),(1+a_(2)x,1+b_(2)x,1+c_(2)x)|=A_(0)+A_(1)x+A_(2)x^(2)+A_(3)x^(3) , then A_(0) is equal to

If (1+x+x^(2))^(n)=b_(0)+b_(1)x+b_(2)x^(2)+….+b_(2n)x^(2n) then prove that b_(1)+b_(3)+b_(5)+…..+b_(2n-1) = (3^(n)-1)/(2)