## 20 Apr Apery's constant

Apery's constant is defined as $$\zeta{(3)}=1.202056\ldots$$, where $$\zeta(x)$$ represents the Euler's zeta function. First lets us define the zeta function. Zeta function is defined as $$\zeta(s)=1+\frac{1}{2^s}+\frac{1}{3^s}+\frac{1}{4^s}+\frac{1}{5^s}+\cdots,$$ where $$s$$ is a complex number. The story of Apery's constant began with the famous Basel problem and Euler's solution...