Explore BrainMass

Explore BrainMass

    A formula that permits to express one class of finite sums in explicit form.

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

    Deduce the recurrent formula for calculation of the finite sums of natural numbers in a natural power:

    1^p + 2^p + 3^p + ... + N^p

    © BrainMass Inc. brainmass.com February 24, 2021, 2:14 pm ad1c9bdddf


    Solution Preview

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


    We denote = p SN , as well as all similar sums with 1 k  p - 1 as k SN .
    We plot then the graph of the function y = x p and mark integer-valued points to build a set of rectangles with the heights equal to n p and the unit length bases.

    It's clear that the total sum of the rectangles ...

    Solution Summary

    A recurrent formula is deduced. The solution is detailed and well presented. A graph is included.