On Error Sums for Square Roots of Positive Integers with Applications to
Lucas and Pell Numbers
Fachhochschule für die Wirtschaft
University of Applied Sciences
Several types of infinite series are considered, which are defined by a
fixed real number α and the denominators and numerators of the
convergents of α. In this paper we restrict α
to the irrational square
roots of positive integers. We express the corresponding error sums in
terms of a finite number of convergents. It is shown that an error sum
formed by convergents with even indices takes only rational values. Two
applications for error sums with α = √ 5 and α = √ 2
are given, where the
convergents are composed of Lucas and Pell numbers, respectively.
Full version: pdf,
(Concerned with sequences
Received September 9 2013;
revised version received January 21 2014.
Published in Journal of Integer Sequences, February 16 2014.
Journal of Integer Sequences home page