Solution 5.1.12.1.

1. \(\frac{1}{(1-x^2)^2}\text{.}\)

2. \(\frac{1}{(1+x)^2}\text{.}\)

3. \(\frac{3x}{(1-x)^2}\text{.}\)

4. \(\frac{3x}{(1-x)^3}\text{.}\) (partial sums).