Recursion formulae for \(\sum_{m=1}^n m^k\) (Q1969405)
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scientific article; zbMATH DE number 1416236
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Recursion formulae for \(\sum_{m=1}^n m^k\) |
scientific article; zbMATH DE number 1416236 |
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Recursion formulae for \(\sum_{m=1}^n m^k\) (English)
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2 July 2000
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Let \(S_k(n)=\sum_{m=1}^n m^k\). The authors prove that \(S_k(n)\) is a \((k+1)\)-th degree polynomial in \(n\) and show that the coefficients of \(S_k(n)\) can be used to obtain the expression of \(S_{k+1}(n)\). A formula for the Bernoulli numbers is also proposed.
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recursion formula
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sum of powers
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Bernoulli numbers
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