 Solution

ID: 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:

a_{n + 1} (ϵ) = o (a_{n} (ϵ)) (ϵ \to 0) .

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

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