收敛速度很快:

\[\frac{1}{\pi}=12\sum_{n=0}^{+\infty}\frac{(-1)^n(6n)!}{(3n)!(n!)^3}\cdot\frac{\color{red}{A}n+\color{green}{B}}{\color{blue}{C}^{3n+\frac{3}{2}}} \]

其中:

\[\color{red}{A}=63365028312971999585426220+28337702140800842046825600\sqrt{5}\\+384\sqrt{5}\sqrt{10891728551171178200467436212395209160385656017 + 4870929086578810225077338534541688721351255040\sqrt{5}},\\ \color{green}{B} = 7849910453496627210289749000+3510586678260932028965606400\sqrt{5}\\+ 2515968\sqrt{3110}\sqrt{6260208323789001636993322654444020882161+ 2799650273060444296577206890718825190235\sqrt{5}},\\ \color{blue}{C}=−214772995063512240− 96049403338648032\sqrt{5} \\− 1296\sqrt{5}\sqrt{10985234579463550323713318473 + 4912746253692362754607395912\sqrt{5}}\]