is there any way to analytically find out at what value the summation of $r^{-r}$ from $r=1$ to infinity converges ? it seems to be around 1.291 if i actually calculate it
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1This series converges extremely rapidly. I don't know if there is a closed form solution, but summing the first $100$ terms, say, would be correct to thousands of digits. – davidlowryduda Feb 17 '23 at 19:00
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@davidlowryduda it would be correct to around 200 digits – Zoe Allen Feb 17 '23 at 19:04
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1What does "analytical" mean here. The actual sum gives an analytical solution, as I would define it. – Thomas Andrews Feb 17 '23 at 19:34