Find the coefficient of `x^(n)` in the power series expansion of `(3x)/((x-1)(x-2)^(2))`.

Find the coefficient of x^(n) in the power series expansion of (x)/((x-1)^(2)(x-2)) specifying the region in which the expansion is valid.

Find the coefficient of x^(3) in the power series expansion of (5x+6)/((x+2)(1-x)) specifying the region in which the expansion is valid.

Find the coefficient of x^(3) in the power series expansion of (5x+6)/((x+2)(1-x)) specifying the region in which the expansion is valid.

Find the coefficient of x^(n) in the power series expansion of (x-4)/(x^(2)-5x+6) specifying the region in which the expansion is valid.

Find the coefficient of x^(n) in the power series expansion of (x-4)/(x^(2)-5x+6) specifying the region in which the expansion is valid.

Find is the coefficient of x^(4) in the power series expansion of (3x^(2)+2x)/((x^(2)+2)(x-3)) specifying the interval in which the expansion is valid.

Find is the coefficient of x^(4) in the power series expansion of (3x^(2)+2x)/((x^(2)+2)(x-3)) specifying the interval in which the expansion is valid.

Find the coefficient of x^(n) in the expansion of (1+x)(1+x)^(n).

(ii) Find the coefficient of x^(n) in the expansion of (x)/((x-1)^(2)(x-2)) in which the expansion is valid.