- #1
Kyousik
- 8
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Homework Statement
f(x) = x^4 / (2 - x^4). Specify radius of convergence.
Homework Equations
Power Series
f`(x) = c2 + 2c2(x-a) + 3c3(x-a)^2 + ... = (infinity)sigma(n=1) [n * cn * (x-a)^(n-1)]
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.