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When I first came across your question, I thought it was a modern-day approximation by somebody using a computer. But when d125q pointed out it was by Ramanujan, then I figured out he must have used a systematic method. One way is to use a Ramanujan-Sato pi formula like, $$\frac{1}{\pi} = \frac{1}{16}\sum_{n=0}^\infty ...



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