Say we have a asypomtotic power series of the general form
$\sum_{n=0}^\infty a_n x^n$
where the $a_n$ are constants and $x$ ist the variable. Suppose the series diverges for a given $x$. Sometimes using least term truncation, one can still finde a more or less optimal solution.
My question is now whether there is an actual proof for that or if that's really just a speculation, though a reasonable one. I've found papers discussing the subject but usually they take very specific examples that i don't find that much helpful.
Thank you!
