In the proof of Jacobi's triple product identity by Jacobi, he considers the infinite product; $\frac{1}{(1-qz)(1-q^2z)...}$ and expands it into 1 + $\frac{B_1z}{(1-qz)}$ + $\frac{B_2z^2}{(1-qz)(1-q^2z)}$ + ..
How did Jacobi know such a product could be expanded in such a way?