The function $f(x) =\frac{5}{1+16x^2}$ is represented by the power series $$\sum_{n=0}^{\infty} c_nx^n$$

I'm supposed to find the first few coefficients of the power series, and these are the answers that I got:
$c_0 = 5$
$c_1 = -80$
$c_2 = 1280$
$c_3 = -20,480$
$c_4 = 327,680$

Yet the WebWork system is saying that $c_1$ through $c_4$ is incorrect.

I've been using this method to find the $n^{th}$ coeffecient: $$\frac{f^{(n)}(c)}{n!}$$

where $c$ the center of the series is $0$.

What am I doing wrong?


Hint: What you wrote are the first five nonzero coefficients.

  • $\begingroup$ @Jordan: Which you calculated correctly. You did some extra work, though. $\endgroup$ Apr 15 '13 at 15:23
  • $\begingroup$ Ah I see. That's very helpful. How do I get all coefficients, including zeroes? I can't seem to figure it out. $\endgroup$
    – Jordan
    Apr 15 '13 at 18:49
  • 1
    $\begingroup$ Never mind. After hours of figuring this out it finally came to me :) thank you for your help. $\endgroup$
    – Jordan
    Apr 15 '13 at 21:10
  • $\begingroup$ @Jordan You're welcome -- the fact is that the several hours of thinking about it is what makes you remember how to do it in the future. $\endgroup$ Apr 16 '13 at 0:01

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