What is the sum of the following series?
$$\sum_{n=1}^{\infty} n^{-n}$$
It definitely converges by ratio test.
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8Sophomore's dream. – Tunk-Fey Jul 07 '14 at 12:36
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Do you have some reason to think there is a closed form? – Gerry Myerson Jul 07 '14 at 12:56
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Many special functions are considered as closed form of infinite series insofar they are referenced as standard functions : http://fr.scribd.com/doc/14623310/Safari-on-the-country-of-the-Special-Functions-Safari-au-pays-des-fonctions-speciales- (table 4a, page 33). This is not yet the case for the so called "Sophomores Dream" function, but that might happen... – JJacquelin Jul 07 '14 at 14:21