If the expression in powers of `x` of the function `1/((1-ax)(1-bx))` is `a_0+a_1 x+a_2 x^2+a_3 x^3+...` then `a_n` is

If cosx=a_0+a_1 x+a_2x^2+... then the value of a_2 is

If (1+x-x^2)^10/(1+x^2)=a_0+a_1x+a_2x^2+...+a_nx^n+… then find a_0+a_1+a_2+… .

If (1+x-x^2)^10/(1+x^2)=a_0+a_1x+a_2x^2+...+a_nx^n+… then find a_1+a_3+a_5+…

If (1+x-x^2)^10/(1+x^2)=a_0+a_1x+a_2x^2+...+a_nx^n+… then find a_0+a_2+a_4+…

If (1+x-x^2)^10/(1+x^2)=a_0+a_1x+a_2x^2+...+a_nx^n+… then find a_0-a_1+a_2_... .

If (1+x)^n=a_0+a_1x+a_2x^2+...+a_nx^n then find : a_1-a_3+a_5-a_7+… .

If (1+x)^n=a_0+a_1x+a_2x^2+...+a_nx^n then find : a_0+a_3+a_6+a_9+… .

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.