Complex analysis taylor series Q

[ElDavidas]

hi, I'm wondering if someone can help me out with this question:

"What are the first two non-zero terms of the Taylor series

$$f(z) = \frac {sin(z)} {1 - z^4}$$ expanded about z = 0.

(Don't use any differentiation. Just cross multiply and do mental arithmetic)"

I know the formula for a Taylor series but I can't see how to do this with just cross multiplying and mental arithmetic.

Thanks

 

[Galileo]

This is a product of two functions: sin(z) and 1/(1-z^4).
If you know the Taylor series of both, you can find their product by 'expanding the brackets'