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Are there any function or infinite series which is known to converge to a value, but whose value of convergence is unknown (impossible to prove)?

pseudobulbose
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  • Just about everything which converges cannot be (explicitly) computed analytically. – Andrew Jun 09 '23 at 18:30
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    The Halting probability is a classic example. There's no algorithm to calculate it to arbitrary precision and in any proof system there's a limit to the lower and upper bound you can prove for it. – AnttiP Jun 09 '23 at 20:11

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