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 \{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}.