For which primes p does the series $\sum_{i=0}^\infty (\frac{10}{11})^i$ converge p-adically and, when it does, to what limit?
2026-04-03 20:55:03.1775249703
For which primes p does the series $\sum_{i=0}^\infty (\frac{10}{11})^i$ converge p-adically
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Hint: $p$-adic analysis is a doll when infinite series is involved since a series converges iff its general term's sequence converges to zero, so the question is:
$$\left(\frac{10}{11}\right)^n\stackrel ?{\xrightarrow[n\to\infty]{}0}\;\;p-\text{adically}$$