Is there any way to express $$\sum_{k=1}^\infty \frac{1}{k^k}.$$ without a sum? I know this converges to ≈ 1,2913 by calculating it, by how can you express this another way? Also, is this number transcendental?
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Very related to "Closed" form for $\sum \frac{1}{n^n}$. – Jeppe Stig Nielsen Jul 29 '13 at 13:52
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Are you interested in this problem from pure curiosity, or do you have a specific reason for wanting to know? – Kenta S Nov 18 '17 at 09:11
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Here's another way: Sophomore's dream.
(From a computational point of view, this may be no more useful than the sum.)
