Question 3 (Sec. 68) in Complex Variables and Applications 9th ed asks
Find the Laurent series that represents the function $f(z)=\frac{1}{z(1+z^2)} $ when $1<|z|<\infty$.
My result works out as $$f(z)=\sum_{n=0}^{\infty}(-1)^n\frac{1}{z^{2n+3}}$$
but the book gives solution as $$f(z)=\sum_{n=1}^{\infty}(-1)^{n+1}\frac{1}{z^{2n+1}}$$ I understand this is just a matter of indexing but is there some sort of pattern or standard choosing of indexing? Some questions' solutions starts infinite sum at $n=0$ while others $n=1$, why is this?