Proof: Sequence (1/n) is a Cauchy Sequence | Real Analysis Exercises

Описание: 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:    • Proof: Archimedean Principle of Real Numbe...  

Intro to Cauchy Sequences:    • Intro to Cauchy Sequences and Cauchy Crite...  
Cauchy Sequences are Bounded:    • Proof: Cauchy Sequences are Bounded | Real...  
Sequence is Cauchy iff it is Convergent:    • Proof: Sequence is Cauchy if and only if i...  

Real Analysis playlist:    • Real Analysis  
Real Analysis Exercises:    • Real Analysis Exercises  

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