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! #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   ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Thanks to Robert Rennie, Barbara Sharrock, and Rolf Waefler for their generous support on Patreon! Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Music Channel:    / @emery3050