Sums of the Powers of Successive Integers

Randolph Nelson
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Chapter Chapter 7 in A Brief Journey in Discrete Mathematics, 2020, pp 93-108 from Springer

Abstract: Abstract What happens when you sum successive powers of integers? To investigate this, define S k , n = 1 + 2 k + 3 k + ⋯ + n k = ∑ i = 1 n i k , k = 0 , 1 , … $$\displaystyle S_{k,n} = 1 + 2^k + 3^k + \cdots + n^k = \sum _{i=1}^n i^k, \ \ \ \ k=0, 1, \ldots $$ An easy program generates the following table of numeric values for small k and n.

Date: 2020
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DOI: 10.1007/978-3-030-37861-5_7

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