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A308915
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Decimal expansion of Sum_{n>=1} 1/(log(n)^log(n)).
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4
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6, 7, 1, 6, 9, 7, 0, 6, 1, 2, 9, 9, 0, 8, 9, 6, 0, 8, 8, 1, 4, 4, 5, 7, 9, 9, 8, 7, 2, 3, 2, 6, 0, 8, 8, 9, 1, 4, 5, 2, 7, 7, 2, 6, 1, 6, 5, 8, 8, 4, 5, 0, 4, 5, 8, 2, 6, 7, 0, 7, 5, 9, 2, 8, 4, 0, 5, 2, 4, 0, 2, 1, 8, 0, 6, 9, 3, 2, 5, 0, 9, 4, 3, 3, 5, 1, 1, 0, 0, 1, 8, 7, 5, 7, 2, 7, 6, 4, 2
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OFFSET
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1,1
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COMMENTS
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This series is convergent because n^2 * 1/log(n)^log(n) = exp(log(n) * (2 - log(log(n)))) which -> 0 as n -> oo.
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REFERENCES
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Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 3.2.1.i p. 279.
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LINKS
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FORMULA
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Equals Sum_{n>=1} 1/(log(n)^log(n)).
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EXAMPLE
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6.71697061299089608814457...
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MAPLE
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evalf(sum(1/(log(n)^log(n)), n=1..infinity), 110);
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MATHEMATICA
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RealDigits[N[1 + Sum[1/Log[n]^Log[n], {n, 2, Infinity}], 100]][[1]] (* Jinyuan Wang, Jul 25 2019 *)
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PROG
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(PARI) 1 + sumpos(n=2, 1/(log(n)^log(n))) \\ Michel Marcus, Jun 30 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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