# Non-convergent power series but good approximation?

Hello,

In my QM class we're using power series which don't converge but apparently still give a good approximation if one only takes the lower-order terms.

Is there any way to understand such a phenomenon? Is it a genuine area of mathematics? Or is it impossible to say something general on this phenomenon?

^ Power series are just polynomials, right? So essentially you're approximating using low-order polynomials. I don't know anything about QM but that'd be my guess as to why what you're doing is reasonable.

AlephZero