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    Using the definition of convergence of a sequence
    show that the following sequences converge to the proposed limit: 1-lim 1/(6n^2+1)=0
    2-lim 2/sqrt[n+3]=0
    3-lim (3n+1)/(2n+5)=3/2

    © BrainMass Inc. brainmass.com March 4, 2021, 6:02 pm ad1c9bdddf
    https://brainmass.com/math/real-analysis/real-analysis-25454

    Solution Preview

    1-
    Let epsilon> 0 and let N be a natural number such that 1/(6N^2)< epsilon. Then if n>= N we will have:
    |1/(6n^2+1)|< |1/(6n^2)|<= |1/(6N^2)|< epsilon
    And that is what we were ...

    Solution Summary

    This uses the definition of convergence of a sequence to show that sequences converge to the proposed limits.

    $2.49

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