You may use that $ 1-x^n = (1-x)(x^{n-1} + x^{n-2}+\cdots +x+1)$
Can someone help me with this one? This is what I have so far:
$ f(x) = \dfrac{1}{x^n(1-x)} = \dfrac{A_0}{x}+\dfrac{A_1}{x^2}+\dfrac{A_2}{x^3}+\cdots +\dfrac{A_{n}}{x^n}+\dfrac{A_{n+1}}{1-x}$.
Multiplying through $ x^n(1-x)$, and rearranging, I get something similar to the hint that was given:
$1-A_{n+1}x^n = (1-x)( A_0x^{n-1} + A_1x^{n-2}+ A_2x^{n-3}+\cdots+A_{n-1}x+A_n)$.
Now I am not sure how to proceed, it's only a 2 point question, so it doesn't seem like it should be difficult, but how do I solve for the constants?
I greatly appreciate any help, point in the right direction!