Using partial fractions, find the Maclaurin series for f(x)=1(1−x)(1−2x)f(x) = \frac{1}{(1-x)(1-2x)}f(x)=(1−x)(1−2x)1.
1+2x+4x2+8x3+⋯1 + 2x + 4x^2 + 8x^3 + \cdots1+2x+4x2+8x3+⋯
1+3x+7x2+15x3+⋯1 + 3x + 7x^2 + 15x^3 + \cdots1+3x+7x2+15x3+⋯
1+x+2x2+4x3+⋯1 + x + 2x^2 + 4x^3 + \cdots1+x+2x2+4x3+⋯
2+5x+11x2+23x3+⋯2 + 5x + 11x^2 + 23x^3 + \cdots2+5x+11x2+23x3+⋯