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Search: id:A130413
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| A130413 |
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Numerators of partial sums for a series for Pi/3. |
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+0
2
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| 1, 19, 47, 1321, 989, 21779, 141481, 1132277, 801821, 91424611, 45706007, 4205393539, 5256312899, 31539920369, 457304942543, 226832956041173, 14176557010703, 28353956712541, 524535004412921, 2098185082863029
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The denominators are given in A130414.
The rationals r(n):= 1+ (4/3)*sum(((-1)^(j+1))/((2*j+1)*((2*j+1)^2-1)),j=1..n), n>=0, have the limit lim(r(n),n->infinity) = Pi/3, approximately 1.047197551.
This series is obtained from the one for Pi/4 (attributed to Nilakantha) obtained by multiplication with 3/4. See the R. Roy reference given in A130411, eq.(13).
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LINKS
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W. Lang, Rationals and limit.
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FORMULA
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a(n)=numerator(r(n)), n>=0, with r(n) defined above.
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EXAMPLE
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Rationals r(n): [1, 19/18, 47/45, 1321/1260, 989/945, 21779/20790, 141481/135135,...].
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CROSSREFS
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Cf. A130411/A130412 (partial sums for a series of 3*(Pi-3)).
Sequence in context: A068474 A141973 A136686 this_sequence A063306 A066775 A118591
Adjacent sequences: A130410 A130411 A130412 this_sequence A130414 A130415 A130416
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jun 01 2007
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