On the alternating sums of reciprocal generalized Fibonacci numbers

TÜRKER ULUTAŞ Y., Kuzuoglu G.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, cilt.15, sa.03, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 03
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1142/s179355712250053x
  • Dergi Adı: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Anahtar Kelimeler: Second-order recurrences, generalized Fibonacci numbers, alternating sums
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.