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Search: id:A099769
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| A099769 |
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Decimal expansion of Sum_{n >= 2} (-1)^n/log(n). |
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+0
1
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| 9, 2, 4, 2, 9, 9, 8, 9, 7, 2, 2, 2, 9, 3, 8, 8, 5, 5, 9, 5, 9, 5, 7, 0, 1, 8, 1, 3, 5, 9, 5, 9, 0, 0, 5, 3, 7, 7, 3, 3, 1, 9, 3, 9, 7, 8, 8, 6, 9, 1, 9, 0, 7, 4, 7, 7, 9, 6, 3, 0, 4, 3, 7, 2, 5, 0, 7, 0, 0, 5, 4, 1, 7, 1, 1, 4, 3, 4, 6, 8, 9, 7, 9, 8, 9, 9, 1, 3, 4, 7, 6, 6, 4, 9, 4, 6, 9, 1, 9, 5, 3, 5, 7, 4, 1
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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A slowly converging series. The reference gives several methods for evaluating the sum.
Mathematica program derived from method #3 in the reference. - Ryan Propper (rpropper(AT)stanford.edu), Sep 25 2006
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REFERENCES
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R. E. Shafer (proposer), Problem 89-15, SIAM Rev., 32 (1990), 481-483.
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EXAMPLE
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0.924299897...
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MATHEMATICA
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Do[X = 2*i; T = Table[Table[0, {X}], {X}]; For[n = 2, n <= X, n++, T[[n, 2]] = Sum[(-1)^k/Log[k], {k, 2, n}]]; For[k = 2, k <= X, k++, For[n = 2, n <= X - k + 1, n++, T[[n, k+1]] = T[[n+1, k-1]] + 1/(T[[n+1, k]] - T[[n, k]])]]; Print[N[T[[2, X]], 50]], {i, 50}] - Ryan Propper (rpropper(AT)stanford.edu), Sep 25 2006
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PROGRAM
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(PARI) sumalt(n=2, (-1)^n/log(n)) - Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007
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CROSSREFS
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Adjacent sequences: A099766 A099767 A099768 this_sequence A099770 A099771 A099772
Sequence in context: A011344 A137197 A133841 this_sequence A020784 A111188 A089065
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KEYWORD
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nonn,cons
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AUTHOR
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njas, Nov 11 2004
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EXTENSIONS
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More terms from Ryan Propper (rpropper(AT)stanford.edu), Sep 25 2006
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007
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