$\sum_{n=1}^{\infty} ka_n$ converges to $kS$ for any nonzero constant $k$

$\lim_{n \to \infty} a_n = 0$

$\sum_{n=1}^{\infty} a_n^2$ must converge

$\sum_{n=1}^{\infty} |a_n|$ must converge