Find a power series representation

Question

Given that 1-x+x²+...+(-x)ⁿ is a power series representation for 1/1+x.

Find a power series representation for x³/1+x²

Answer 1

This problem is not too difficult. Notice that we can get to the given function by multiplying the original function by x^3. The tells you that you can get the series you want by multiply each term of the original series by x^3.