All Questions

Suppose $f(x)=\prod_{k=1}^n(x-a_k)$ where all $a_k>0$. Expand the function $\frac1f$ at $\infty$ so that $$\frac1{f(x)}=\frac{b_n}{x^n}+\frac{b_{n+1}}{x^{n+1}}+\cdots.$$ Does it follow that each $...