In mathematics, Faulhaber's formula, named after the early 17th century mathematician Johann Faulhaber, expresses the sum of the p {\displaystyle p} th powers of the first n {\displaystyle n} positive integers ∑ k = 1 n k p = 1 p + 2 p + 3 p + ⋯ + n p {\displaystyle \sum _{k=1}^{n}k^{p}=1^{p}+2^{p}+3^{p}+\cdots +n^{p}} as a polynomial in n {\displaystyle n} . In modern notation, Faulhaber's formula is ∑ k = 1 n k p = 1 p + 1 ∑ r = 0 p ( p + 1 r ) B r + n p + 1 − r .
In mathematics, Faulhaber's formula, named after the early 17th century mathematician Johann Faulhaber, expresses the sum of the p {\displaystyle p} th powers of the first n {\displaystyle n} positive integers ∑ k = 1 n k p = 1 p + 2 p + 3 p + ⋯ + n p {\displaystyle \sum _{k=1}^{n}k^{p}=1^{p}+2^{p}+3^{p}+\cdots +n^{p}} as a polynomial in n {\displaystyle n} . In modern notation, Faulhaber's formula is ∑ k = 1 n k p = 1 p + 1 ∑ r = 0 p ( p + 1 r ) B r + n p + 1 − r .
Source: Wikipedia "Faulhaber's formula" · CC BY-SA 4.0
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