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## Main Question or Discussion Point

Perturbation theory provides good answers as long as the contributions get smaller and smaller as we go to higher and higher orders. Then we only need to compute the first few diagrams to get accurate results.

Is it possible for a perturbation series to get bigger then smaller then bigger-it wouldn't have a finite sum unless some terms were negative, but could such a perturbation expansion be useful in physics?

Is it possible for a perturbation series to get bigger then smaller then bigger-it wouldn't have a finite sum unless some terms were negative, but could such a perturbation expansion be useful in physics?