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Proof: Sequence (1/n) is a Cauchy Sequence | Real Analysis Exercises
We prove the sequence {1/n} is Cauchy using the definition of a Cauchy sequence! Since (1/n) converges to 0, it shouldn't be surprising that the terms of (1/n) get arbitrarily close together, and as we have proven (or will prove, depending where you're at), convergence and Cauchy-ness are equivalent, so (1/n) is Cauchy - let's prove it! # ...
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