On the alternating sums of reciprocal generalized Fibonacci numbers

TÜRKER ULUTAŞ Y., Kuzuoglu G.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, vol.15, no.03, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 03
  • Publication Date: 2022
  • Doi Number: 10.1142/s179355712250053x
  • Journal Name: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: Second-order recurrences, generalized Fibonacci numbers, alternating sums
  • Kocaeli University Affiliated: Yes

Abstract

In this paper, we consider finite alternating sums derived from the generalized Fibonacci numbers Sigma(mn)(k=n)(-1)(k)/U-k, Sigma(mn)(k=n)(-1)(k)/U-2k and Sigma(mn)(k=n)(-1)(k)/U2k-1, where m and n are positive integers with m >= 2, n >= 2. Applying the greatest integer function to these sums, we obtain some equalities involving the generalized Fibonacci numbers.