Sequence of P-adic Integers has Convergent Subsequence/Proof 1

Lemma 4
From P-adic Expansion Converges to P-adic Number:
 * $\ds \sum_{n \mathop = 0}^\infty b_n p^n$ converges to some $x \in \Q_p$

By definition of $p$-adic integer:
 * $x \in \Z_p$