1. The problem statement, all variables and given/known data f(x) = x^4 / (2 - x^4). Specify radius of convergence. 2. Relevant equations Power Series f`(x) = c2 + 2c2(x-a) + 3c3(x-a)^2 + .... = (infinity)sigma(n=1) [n * cn * (x-a)^(n-1)] 3. The attempt at a solution I'm not sure what to do. Usually, most problems are like x^3 / x^4, so I'm not sure what to do. Using L'Hoptials, differentiating top and bottom doesn't do much. Like if it were x / (9+x^2). I could easily pull out an x and a 9 (x/9) * [1/ [1-(-x/3)^2] ] Then look at just the -(x/3)^2 as a geometric series |-(x/3)^2| < 1 = |x^2| / 9 < 1 |x^2| < 9 -3 < x < 3 R = 3 and I = -3, 3 But not sure what to do with the one above in how to manipulate it.