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**Lord Darkin** 1. Find the first five terms in the Taylor series about x = 0 for $\displaystyle f(x) = \frac{1}{1-2x}$ 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 $\displaystyle g(x) = \frac{1}{(1-2x)(1-x)}.$

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.)