Biểu thức sau đây hội tụ về √2:

2 = 3 2 − 2 ( 1 4 − ( 1 4 − ( 1 4 − ( 1 4 − ⋯ ) 2 ) 2 ) 2 ) 2 = 3 2 − 4 ( 1 8 + ( 1 8 + ( 1 8 + ( 1 8 + ⋯ ) 2 ) 2 ) 2 ) 2 . {\displaystyle {\begin{aligned}{\sqrt {2}}&={\tfrac {3}{2}}-2\left({\tfrac {1}{4}}-\left({\tfrac {1}{4}}-\left({\tfrac {1}{4}}-\left({\tfrac {1}{4}}-\cdots \right)^{2}\right)^{2}\right)^{2}\right)^{2}\\&={\tfrac {3}{2}}-4\left({\tfrac {1}{8}}+\left({\tfrac {1}{8}}+\left({\tfrac {1}{8}}+\left({\tfrac {1}{8}}+\cdots \right)^{2}\right)^{2}\right)^{2}\right)^{2}.\end{aligned}}}