[mkarrmann]

Why do you think a series which absolutely converges but whose first few terms are a poor approximation is related to a series which diverges but whose first few terms match the empirically expected value?

Not only is it a stretch to wonder about parallels between a basic Calc II concept and Quantum Field Theory, but is seems like the exponential function is the exact opposite of the example you provided.

[antognini]

I was being a bit loose in my language, but I was more specifically thinking of the connection to "resurgence theory" which aims at understanding more complicated kinds of apparently divergent infinite sums. See this article for a popular overview: https://www.quantamagazine.org/alien-calculus-could-save-par...