I need some help to prove that the power series of $\coth x$ is:
$\frac{1}{x} + \frac{x}{3} - \frac{x^3}{45} + O(x^5) \ \ \ \ \ $
I don't know how to derive this, should I divide the expansion of $\cosh(x)$ by the expansion of $\sinh(x)$? (I've tried but without good results :( )
Or I have to use residue calculus?
Anyone can suggest me a link where I can find a detailed explanation of this expansion?
Thanks.