Advanced Calculus Analysis : Cauchy and Convergent Sequences
We proved the following theorem in the class: "If a>0 and if a sequence... is covergent, then the sequence... is convergent." In proving this theorem, we proved that... is Cauchy instead of proving it converges directly. Why did we have to do that?
Please see attachment for full question.
© BrainMass Inc. brainmass.com March 4, 2021, 6:08 pm ad1c9bdddfhttps://brainmass.com/math/calculus-and-analysis/advanced-calculus-analysis-cauchy-convergent-sequences-30965
Solution Preview
Please see the attachment.
Theorem: Suppose and the sequence converges. Show that the sequence converges.
Proof:
First, I claim that if , then . This is true because is a ...
Solution Summary
Cauchy and Convergent Sequences are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.
$2.49