die Folge der Partialprodukte

\begin{eqnarray}{v}_{n}=\displaystyle \prod _{k=1}^{n}\frac{{a}_{k}}{2}\end{eqnarray}

\begin{eqnarray}\begin{array}{rcl}{a}_{1} & = & \sqrt{2},\\ {a}_{k+1} & = & \sqrt{2+{a}_{k}}\quad(k\in {\mathbb{N}}).\end{array}\end{eqnarray}

\begin{eqnarray}{4}^{n}\left({v}_{n}-\displaystyle \frac{2}{\pi}\right)\to \displaystyle \frac{\pi}{12}\quad{\text{f}}{\rm{\ddot {u}}}{\text{r}}\quad{n\to \infty},\end{eqnarray}

\begin{eqnarray}{v}_{n}\to \displaystyle \frac{2}{\pi}\end{eqnarray}