First, we need to write down the power series expansion for 1/(1-t)

This series is centered at 0, so, for simplicity, we'll begin with the series that is also centered at 0: 2/(1-x)^3

Compare 1/(1-x) to 2/(1-x)^3 Right off the bat, we can see that these two are very similar.

Step 1: Multiply 1/(1-x) by 2.

Result: 2/(1-x)

Step 2: Multiply by 1/(1-x)^2

Result: 2/(1-x)^3

The two equations are now the same. Apply these steps to the above listed series. Multiply the series by 2 and then by 1/(1-x)^2. This will give you a power series expansion for the equation 2/(1-x)^3

The first one is solved in the same method. Alternatively, you could solve by taking the definition of a power series. However, they asked for you to solve it in the above manner, so I suggest doing it that way.