A formula that permits to express one class of finite sums in explicit form.
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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
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Solution.
We denote = p SN , as well as all similar sums with 1ï‚£ k ï‚£ 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.
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