Explore BrainMass

Explore BrainMass

    Advanced Calculus Analysis : Cauchy and Convergent Sequences

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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 ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/advanced-calculus-analysis-cauchy-convergent-sequences-30965

    Attachments

    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

    ADVERTISEMENT