1. The problem statement, all variables and given/known data Okay, first there is an explanation of the Taylor Series equation. This I don't have a problem with. Then, we have this: Consider the power series 2 - (2/3)x + (2/9)x^2 - (2/27)x^3. What rational function does this power series represent? 2. Relevant equations / 3. The attempt at a solution I basically am just stuck at the end. I do understand how this function relates to the Taylor Series equation and wrote a detailed explanation of what parts represent a, i, f(a), f'(a), etc. However, after solving and presenting this information: f(a) = 2 f'(a) = -2/3 f''(a) = 4/9 f'''(a) = -12/27 I don't know how to sort of reverse it and find the relevant function. I know that the numerator is being multiplied by -1, then -2, then -3, and the denominator is being multiplied by 3, but how does one take that information and turn it into equations? I don't want the answer - I just want a hint in the right direction, or a method by which I can find it. Thank you guys.