Apéry's constant

In mathematics, Apéry's constant is the infinite sum of the reciprocals of the positive integers, cubed. That is, it is defined as the number

${\displaystyle {\begin{aligned}\zeta (3)&=\sum _{n=1}^{\infty }{\frac {1}{n^{3}}}\\&=\lim _{n\to \infty }\left({\frac {1}{1^{3}}}+{\frac {1}{2^{3}}}+\cdots +{\frac {1}{n^{3}}}\right),\end{aligned}}}$

where ζ is the Riemann zeta function. It has an approximate value of

ζ(3) ≈ 1.202056903159594285399738161511449990764986292… (sequence A002117 in the OEIS).

It is named after Roger Apéry, who proved that it is an irrational number.