I have a really clever solution to this problem but it doesn’t fit in a tweet.
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I think everyone is looking for a rigorous analytical proof.
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I think it depends on the rational approximations to Pi. Because it won't be convergent if the denominator part becomes 0 implying that the sin function gives 0. Why can't we just use a supercomputer and observe its behavior up to some gigantic range of values?
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As you guessed, convergence of this series is just a bizarre reformulation of a statement about how π can be approximated by rationals, namely that its "approximation exponent" is less than 5/2. But there is no doubt in anyone's mind that it's really 2, and series converges. …
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Doesn't look like it'll converge. Small, though.pic.twitter.com/id0LNsjXMW
Thanks. Twitter will use this to make your timeline better. UndoUndo
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Seems to converge to somewhere near 30.3145 but no idea whypic.twitter.com/W7siejlMWx
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But but ... Why not `sum += term;`? Why the extra characters!?!?!??
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It's called Flint Hills series. Alekseyev in 2011 has shown that the question of the convergence of the Flint Hill series is related to the irrationality measure of π
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Don't confuse it with the Flint HillS series!
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