# Convergent series in the p-adic completion of Q

Prove that if the sequence $\{t_k\}_{k \in N} \subset \mathbb{Q}$ has the property that $|t_k|_p \to 0$ as $p \to \infty$, then the series $\sum_{k=1}^{\infty}t_k$ converges in the p-adic completion $\mathbb{Q}_p$ of $\mathbb{Q}$.