Chudnovsky Formula for ∏
Two brothers, David and Gregory Chudnovsky, published the following formula for 
in 1988, based Ramanujan’s work:
![\[\frac{1}{\pi}=12\sum_{k=0}^{\infty}\frac{{(-1)^k}{(6k)!(13591409+545140134k)}}{(3k)!{(k!)^3}640320^{3k+3/2}}\]](https://oopstart.com/wp-content/ql-cache/quicklatex.com-b17ecbd10f9f1db095a7488596bc859c_l3.png "Rendered by QuickLaTeX.com")
A year later, they used it to compute to 1 billion decimal places.
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