Explore BrainMass

Explore BrainMass

    Series Convergence: Two-sided Estimator

    Not what you're looking for? Search our solutions OR ask your own Custom question.

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

    Please see the attached file for the fully formatted problems.

    A simple technique to estimate values of the finite sums of reciprocals to natural numbers raised to positive power and to define if corresponding infinite series converge.

    Deduce two-sided estimator for the sums of the positive powers (p) of reciprocals to natural numbers
    to prove convergence of corresponding series for p more than 1, and divergence of the series for [EQUATION].

    © BrainMass Inc. brainmass.com May 24, 2023, 1:00 pm ad1c9bdddf


    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.


    To deduce the two-sided estimator for
    = ,
    we plot the graph of the function for x  0:

    Total square of all rectangles with vertexes below the curve is equal to and is obviously less than the value of the ...

    Solution Summary

    A two-sided estimator is used to prove divergence of a summation.
    The solution is detailed and well presented.