Given any computable function $f(x)$, is there an algorithm to find a set of coefficients $a_n$, such that
i) $g(x)=\sum_{n=1}^{n=\infty} a_nx^n$ converges for all $x>1$
ii) $g(x)$ eventually dominates $f(x)$
If not, is there a way to approach this boundary from above or below?