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    Cauchy and sequences

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    Respected Sir / Madam,

    I need following question to be answered.

    Please mention each and every step. Please explain every thing.
    Text Book:- Taylor & Menon.
    Page 523 Exercise Problem.

    Page 526 Exercise Problem

    Thanking you

    © BrainMass Inc. brainmass.com March 4, 2021, 8:25 pm ad1c9bdddf


    Solution Preview

    Please see the attachment.

    Page 523
    Since , and for , then we have

    Then we get the absolute value on both sides and get

    In general, we have

    Now we consider and without generality, we assume , where is a nonnegative integer. Then we have


    Solution Summary

    This shows how to prove that Cauchy's condition is fulfilled and complete a proof regarding a set and intervals.