Problem

Another quadratically convergent scheme for computing π was discovered by Borwein and Bo...

Another quadratically convergent scheme for computing π was discovered by Borwein and Borwein [1984] and can be written as

Numerically verify that |x − π|?102k . Note: Ludolf van Ceulen (1540–1610) was able to calculate π to 36 digits. With modern mathematical software packages such as MATLAB, Maple, and Mathematica, anyone can easily compute π to tens of thousands of digits in seconds!

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