Is there a known evaluation of $$\sum_{k=1}^{\infty} \frac{1}{k^k}$$
Wolfram Alpha says that it converges to $\approx 1.29129$.
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6Sophomore's dream. – achille hui Jun 27 '14 at 05:47
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3This is not so easy to find if you don't know what it's called. IMHO it could do without the downvotes. – David Jun 27 '14 at 05:50
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@David: You're right, but I think the downvotes are aimed at the poor formulation of the question. – Raskolnikov Jun 27 '14 at 05:51
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@achillehui:But is there anyway to integrate that integral though? – Gina Jun 27 '14 at 06:21
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@Gina, I don't think so. The sum itself converges very rapidly. Summing the first 60 terms or so already give you a number accurate to $> 100$ decimal places. There isn't too much point to find another way. – achille hui Jun 27 '14 at 09:55