/sci/ - Science & Math

>>8348342
>>8348665
>>8348600

Self study dumbie me is back with another one.

Laurent series for [math] \frac{1}{z^2-4} \text{ about } z = 2. [/math]

I decompose [math] \frac{1}{(z-2)^{2}-4} = \frac{1}{z(z-4)} [/math] into partial fractions and get a strictly negative series even though it should be alternating apparently. The book's answer is
[math] \sum\limits_{k=-1}^{\infty}{\frac{-1^{k+1}(z-2)^{k}}{4^{k+2}}} [/math] I just don't see how it's alternating. Does anyone recommend any practice resources also to refine my skills with series manipulations? Seems like I lost a bit of it if I need to keep asking this shit.