In mathematics, Faulhaber's formula, named after Johann Faulhaber, expresses the sum
as a (p + 1)th-degree polynomial function of n, the coefficients involving Bernoulli numbers Bj.
The formula says
Faulhaber himself did not know the formula in this form, but only computed the first seventeen polynomials; the general form was established with the discovery of the Bernoulli numbers (see History section below). The derivation of Faulhaber's formula is available in The Book of Numbers by John Horton Conway and Richard K. Guy.
Read more about Faulhaber's Formula: Alternate Expression, Examples, Proof, Relation To Bernoulli Polynomials, Umbral Form, Faulhaber Polynomials, History
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“My formula for greatness in human beings is amor fati: that one wants to change nothing, neither forwards, nor backwards, nor in all eternity. Not merely to endure necessity, still less to hide it—all idealism is mendacity in the face of necessity—but rather to love it.”
—Friedrich Nietzsche (1844–1900)