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
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Sep 21 2013
STATUS
approved