Inspired by The set of all limits of sub-series of an absolute convergent series is the following true?:

Let $a_n$ be a strictly decreasing sequence and $\sum_1^\infty a_n=\ell<\infty$ is a convergent series. Is it true to say that the set of all possible value of all subseries $\sum a_{n_i}$ of $\sum a_n$ is whole $[0,\ell]$?