##
**
On Error Sums for Square Roots of Positive Integers with Applications to
Lucas and Pell Numbers
**

###
Carsten Elsner

Fachhochschule für die Wirtschaft

University of Applied Sciences

Freundallee 15

D-30173 Hannover

Germany

**Abstract:**

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,
dvi,
ps,
latex
**

(Concerned with sequences
A000032
A000045
A000129
A040968
A235861.)

Received September 9 2013;
revised version received January 21 2014.
Published in *Journal of Integer Sequences*, February 16 2014.

Return to
**Journal of Integer Sequences home page**