Biểu thức bình phương lồng nhau sau tiến về √3:

  3 = 2 − 2 ( 1 2 − ( 1 2 − ( 1 2 − ( 1 2 − … ) 2 ) 2 ) 2 ) 2 = 7 4 − 4 ( 1 16 + ( 1 16 + ( 1 16 + ( 1 16 + … ) 2 ) 2 ) 2 ) 2 . {\displaystyle \!\ {\sqrt {3}}=2-2\left({\frac {1}{2}}-\left({\frac {1}{2}}-\left({\frac {1}{2}}-\left({\frac {1}{2}}-\dots \right)^{2}\right)^{2}\right)^{2}\right)^{2}={\frac {7}{4}}-4\left({\frac {1}{16}}+\left({\frac {1}{16}}+\left({\frac {1}{16}}+\left({\frac {1}{16}}+\dots \right)^{2}\right)^{2}\right)^{2}\right)^{2}.}