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