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! #RealAnalysis

Besides the definition of Cauchy, the only thing we need is the Archimedean principle, proven here: [ Ссылка ]

Intro to Cauchy Sequences: [ Ссылка ]
Cauchy Sequences are Bounded: [ Ссылка ]
Sequence is Cauchy iff it is Convergent: [ Ссылка ]

Real Analysis playlist: [ Ссылка ]
Real Analysis Exercises: [ Ссылка ]

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