I am trying to prove that if we have $\sum|{r_j}| < R$, and $|\{s_{j,k}\}| \le S $, and if $\lim_{k \to \infty} s_{j,k} = 0$ for every element j, that the limit as k goes to infinity of $\sum^{\infty}_{j=0}r_j s_{j,k}$ is $0$. I am a bit stuck. I am trying to use basic properties of the convergence of sequences and series as given in Rudin's PMA, but keep running into trouble.
2026-03-28 10:17:18.1774693038
multiplying a convergent sequence by a convergent series
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