[" If "],[(1)/(1-2x+x^(2))=1+b_(1)x+b_(2)x^(2)+b_(3)x^(3)+....oo],[|x|<1]

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+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)

The value of |(a_(1) x_(1) + b_(1) y_(1),a_(1) x_(2) + b_(1) y_(2),a_(1) x_(3) + b_(1) y_(3)),(a_(2) x_(1) +b_(2) y_(1),a_(2) x_(2) + b_(2) y_(2),a_(2) x_(3) + b_(2) y_(3)),(a_(3) x_(1) + b_(3) y_(1),a_(3) x_(2) + b_(3) y_(2),a_(3) x_(3) + b_(3) y_(3))| , is

The value of |(a_(1) x_(1) + b_(1) y_(1),a_(1) x_(2) + b_(1) y_(2),a_(1) x_(3) + b_(1) y_(3)),(a_(2) x_(1) +b_(2) y_(1),a_(2) x_(2) + b_(2) y_(2),a_(2) x_(3) + b_(2) y_(3)),(a_(3) x_(1) + b_(3) y_(1),a_(3) x_(2) + b_(3) y_(2),a_(3) x_(3) + b_(3) y_(3))| , is

Suppose a_(1)+a_(2)+a_(3)+1.3,b_(1)+b_(2)+b_(3)=2.1,c_(1)+c_(2)+c_(3)=1.6 and Delta(x)=|(1+a_(1)x,1+b_(1)x,1+c_(1)x),(1+a_(2)x,1+b_(2)x,1+c_(3)x),(1+a_(3)x,1+b_(3)x,1+c4x)| =A_(0)+A_(1)x+A_(2)x^(2)+A_(2)x^(3) , then A_(1)= _________

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.

(1)(a+b)+(a^(2)+2b)+(a^(3)+3b)+.... upto n terms =(2)(x+(1)/(x))^(2)+(x^(2)+(1)/(x^(2)))^(2)+(x^(3)+(1)/(x^(3)))^(2)+...(x^(n)+(1)/(x^(n)))^(2)=

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))):}|