I was trying to solve and ODE and while doing some asymptotics, I bumped into something like this $\left(1+\frac{\gamma}{z_{0}}+\epsilon \frac{z_{1}}{z_{0}}\right)^{-2}$
where $\gamma$ $\,$ is of $\mathcal{O}(1)$. To my understanding, the expansion of the latter would be $\left(1+\frac{\gamma}{z_{0}}\right)-2\epsilon\frac{z_{1}}{z_{0}}+\ldots$
The above doesn't feel right to me though! How would one go about something like this?
$\gamma$,$z_{0}$ and $z_{1}$ are all $\mathcal{O}(1)$ apart from $\epsilon$ where we take the latter as small.