Past exam of the perturbation methods and applied complex variables course of the University of Oxford / 2008 / A / 1 / i / Solution

For each fixed $n$, the next term must be negligible relative to its predecessor:The ratios are understood where their denominators are nonzero near the limiting point, or equivalently through the little o notation definition. For example $1,ϵ,{ϵ}^2,\dots$ form an asymptotic sequence.