Continued fraction : $\zeta(2)=[a_0,a_1,a_2,a_3,\dots]=[1,1,1,1,4,2,4,7,1,4,\dots]$
$k$-th approximation $\frac{p_k}{q_k}$ : $\frac{p_0}{q_0}<\frac{p_2}{q_2}<\cdots<\zeta(2)<\cdots<\frac{p_3}{q_3}<\frac{p_1}{q_1}$
$p_k=a_k p_{k-1}+p_{k-2},$ $p_{-1}=1,p_{-2}=0,$ $q_k=a_k q_{k-1}+q_{k-2},$ $q_{-1}=0,q_{-2}=1$