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A229351
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Numerators of the ordinary convergents of continued fraction [2/1, 3/2, 4/3, 5/4,...].
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6
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2, 4, 9, 2, 4, 5, 9, 7, 4, 6, 0, 2, 1, 2, 8, 6, 6, 0, 3, 3, 9, 6, 8, 5, 1, 8, 3, 2, 3, 9, 1, 5, 0, 8, 5, 2, 2, 6, 6, 0, 6, 4, 3, 8, 9, 0, 5, 2, 9, 8, 4, 8, 0, 2, 5, 5, 5, 3, 3, 5, 2, 3, 5, 8, 0, 0, 6, 2, 2, 1, 6, 1, 9, 2, 9, 2, 6, 8, 2, 3, 8, 8, 6, 9, 5, 2
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OFFSET
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1,1
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COMMENTS
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Suppose that x(n) is a sequence of positive real numbers with divergent sum. By the Seidel Convergence Theorem, the continued fraction [x(1),x(2),x(3),...] converges.
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LINKS
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EXAMPLE
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[2/1, 3/2, 4/3, 5/4, ...] = 2.492459746021286... The first 5 ordinary convergents are 2, 5/2, 162/65, 167/67, 329/132.
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MATHEMATICA
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z = 500; t = Table[(n+1)/n, {n, z}]
r = FromContinuedFraction[t]; c = Convergents[r, z];
RealDigits[r, 10, 120] (* A229353 *)
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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