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**Consider the sequence s_n = Ʃ (k=0 to n) (t_k * p^k) in Q(rationals) with the p-adic metric (p is prime); where t_n is the sequence 1,2,1,1,2,1,1,1,2,... Show that s_n is Cauchy, but [s_n] (the equivalence class of s_n) cannot be expressed by a rational number.**

As far as what I know: I'm familiar with the p-adic metric, and what a cauchy sequence is. I just cant think of how to show that s_n is cauchy.

Thank you very much for any advice and hints.