Prove Sequence Diverges with Subsequences | Real Analysis

Support the production of this course by joining Wrath of Math to access all my real analysis videos plus the lecture notes at the premium tier!    / @wrathofmath   🛍 Get the coolest math clothes in the world! https://mathshion.com/ Real Analysis course:    • Real Analysis   Real Analysis exercises:    • Real Analysis Exercises   Get the textbook! https://amzn.to/3CMdgjI We can use subsequences to prove a sequence diverges! We'll go over how and why in today's real analysis video lesson. This all comes from the subsequence limit theorem we proved, stating that a sequence converges to L if and only if every subsequence converges to L. Then the idea is as follows. If two subsequences have different limits, they certainly don't all converge to L, and thus the original sequence can't converge to L. Or, if a subsequence diverges, certainly not all subsequences converge to L, and so the original sequence can't converge to L. In this way, we can prove a sequence diverges by finding two subsequences with different limits, or by finding a divergent subsequence. #RealAnalysis Intro to Subsequences:    • Intro to Subsequences | Real Analysis   Sequence Converges if and only if all its Subsequences Do:    • Sequence Converges iff Every Subsequences ...   Proving (-1)^n Diverges using Subsequences:    • Sequence (1^n) Diverges using Subsequences...   Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu