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A229353
Decimal expansion of continued fraction [2/1, 3/2, 4/3, 5/4,...].
3
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, 4, 4, 9, 5, 3, 0, 7, 0, 5, 5, 2, 3, 9, 3, 7, 8, 6, 0, 4, 3, 3, 7, 9, 1, 4, 9, 8, 5, 6, 0, 0, 9, 5, 1, 3, 9, 7, 9, 6, 9, 5, 2, 6, 9, 5, 2, 6, 6, 7, 7, 6
OFFSET
1,1
COMMENTS
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.
EXAMPLE
[2/1, 3/2, 4/3, 5/4, ...] = [2,2,32,1,1,1,9,5,1,1,2,1] = 2.492459746021286603... The first 5 ordinary convergents are 2, 5/2, 162/65, 167/67, 329/132.
MATHEMATICA
z = 500; t = Table[(n+1)/n, {n, z}]
r = FromContinuedFraction[t]; c = Convergents[r, z];
Numerator[c] (* A229351 *)
Denominator[c] (* A229352 *)
RealDigits[r, 10, 120] (* A229353 *)
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Sep 21 2013
STATUS
approved