Series of Error Terms for Rational
Approximations of Irrational Numbers
Fachhochschule für die Wirtschaft Hannover
-th convergent of a real irrational
, and let
this paper we investigate various sums of the type
. The main subject of the paper is bounds for
these sums. In particular, we investigate the behaviour of such sums
is a quadratic surd. The most significant properties of
the error sums depend essentially on Fibonacci numbers or on related
Full version: pdf,
(Concerned with sequences
Received July 12 2010;
revised version received January 10 2011.
Published in Journal of Integer Sequences, January 28 2011.
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