# How to construct an open cover from a series

Let be $$[a,b]subseteq mathbb{R}$$ and $$sumlimits_{i=1}^{infty}a_i$$ a convergent series.

How do I construct an open cover of $$[a,b]$$ by means of the series $$sumlimits_{i=1}^{infty}a_i$$?