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    Proof: Upper and lower limits

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    Please see the attached file for the fully formatted problems.

    Let be a sequence of real numbers.

    We define

    and

    I'm having trouble with the following three proofs:

    1) Show that
    2) Show that if the limit of only exists when , then .
    3) Show that if , then the limit exists, and .

    © BrainMass Inc. brainmass.com November 29, 2021, 11:55 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/proof-upper-lower-limits-10178

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    Let be a sequence of real numbers.

    We define

    and

    I'm having trouble ...

    Solution Summary

    Proofs are provided for three statements involving limits. The solution is detailed and well presented.

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