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[What happens when you sum successive powers of integers? To investigate this, define Sk,n=1+2k+3k+⋯+nk=∑i=1nik,k=0,1,…\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\displaystyle S_{k,n} = 1 + 2^k + 3^k + \cdots + n^k = \sum _{i=1}^n i^k, \ \ \ \ k=0, 1, \ldots $$ \end{document} An easy program generates the following table of numeric values for small k and n.]
Published: Feb 12, 2020
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