1. Find the first five terms in the Taylor series about x = 0 for

and find the interval of convergence for the series.

2. Then, using partial fractions, find the first five terms in the Taylor series about x = 0 for

Originally I took the first four derivatives of f(x), plugged in x=0 for them, then used those 5 results (four derivatives + original) to get the first five terms. However, my teacher told me that was incorrect, so I instead just plugged in x=0, x=1, up to x=4 into f(x) to get 1, -1, -1/3, -1/5, -1/7. Is that right?

(I've got issues with later parts too but I want to clear up the first part.)