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Given $f(x) = \dfrac{4x+53}{x^2-x-30}$, display it as a power series and find the radius of convergence. then calculate $f^{(20)}(0)$

So what I did was look at the Taylor Series Formula: $$f(x) = \sum_{n=0}^{\infty} {\frac{f^{n}(0)}{n!} x^n } $$

$f(0) = \dfrac{53}{-30}$ and $f'(0) = \dfrac{-67}{(-30)^2}$.

But after that it only gets harder and harder to derive, thus making it harder to see a general form of the $n$th derivative.

Would be happy if someone gave me a direction. Thank you

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A related problem. – Mhenni Benghorbal May 22 '13 at 13:09

Hint: Use partial fractions, and write it as the sum of geometric series. Result:


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(+1) good hint. – Mhenni Benghorbal May 22 '13 at 13:09

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