Convergence radius of a perturbation series

[wdlang]

i see people discussing the convergence radius of a perturbation series in the literature

i am really baffled

generally, one can only get the first few coefficients of a perturbation series

that is, the perturbation series is not known at all

how can one determine the convergence radius of the series at all?

what is the point of determine the radius if only a few first coefficients are available?

 

[hunt_mat]

In general perturbation expansions aren't convergent, there will be a term which after that that series starts growing.