If `1/(1-2x+x^2)=1+b_1x+b_2x^2+b_3x^3+..oo`, `|x|<1`, then the value of `b_1` is

If x is small and if the expansion of a + (b)/(1 + 2x) + ( c)/(1 -3x^2) is 1 + x + 2x^2 + ……oo find (a,b,c)

If 1/((1-2x)(1+3x))=A/(1-2x)+B/(1+3x) , then 2B =

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.

If, y=x-x^2/2+x^3/3-x^4/4+....oo and (|x|lt1) then x=y+y^2/(a!)+y^3/(b!)+......+oo Find a^2+b

If (1 -2x)/(3 + 2x - x^(2)) = (A)/(3 -x ) + (B)/(x + 1) ,then the value of A + B is

If a,b,c are in A.P .and f(x)=|[x^2+x+a+1, x^2+1, 1] , [2x^2+x+b-1, 2x^2-1, 1] , [3x^2+x+c-2, 3x^2-2, 1]| then f'(x) is