Prove Sequence Diverges with Subsequences | Real Analysis

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Real Analysis course:    • Real Analysis  
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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...  

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