Q:

Subsequential Limits of a Conditionally Convergent Sequence

Let $\sum_{x=1}^\infty a_n$ be a conditionally convergent series of real numbers. Let $(s_n)$ be the sequence of $n$-th partial sums. Let $S$ be the set of all subsequential limits of $(s_n)\subset\mathbb{R}$. 
Is there anything that can be said about $S$? Does it equal $\mathbb{R}$ by any consequence of the Riemann Series Theorem?

A:

$s_n$ tends to a finite limit $s$. So all subsequence of $\{s_n\}$ converge to $s$ and the set of limits of subsequences is $\{s\}$. 

