Convergent series in the p-adic completion of Q

Hi there, I've got a question on p-adic numbers which make pretty much no sense to me so I have no idea what to do or why, any help appreciated.

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