Partial Sums of P-adic Expansion forms Coherent Sequence

Theorem
Let $p$ be a prime number.

Let $\displaystyle \sum_{n \mathop = 0}^\infty d_n p^n$ be a $p$-adic expansion.

Let $\sequence{\alpha_n}$ be the sequence of partial sums; that is:
 * $\forall n \in \N :\alpha_n = \displaystyle \sum_{i \mathop = 0}^n d_i p^i$.

Then $\sequence{\alpha_n}$ is a coherent sequence.