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