On the Reciprocal Sums of Products of Two Generalized Bi-Periodic Fibonacci Numbers
نویسندگان
چکیده
This paper concerns the properties of generalized bi-periodic Fibonacci numbers {Gn} generated from recurrence relation: Gn=aGn−1+Gn−2 (n is even) or Gn=bGn−1+Gn−2 odd). We derive general identities for reciprocal sums products two numbers. More precisely, we obtain formulas integer parts ∑k=n∞(a/b)ξ(k+1)GkGk+m−1,m=0,2,4,⋯, and ∑k=n∞1GkGk+m−1,m=1,3,5,⋯.
منابع مشابه
Alternating sums of reciprocal generalized Fibonacci numbers
ABSTRACT Recently Holliday and Komatsu extended the results of Ohtsuka and Nakamura on reciprocal sums of Fibonacci numbers to reciprocal sums of generalized Fibonacci numbers. The aim of this work is to give similar results for the alternating sums of reciprocals of the generalized Fibonacci numbers with indices in arithmetic progression. Finally we note our generalizations of some results of ...
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ژورنال
عنوان ژورنال: Mathematics
سال: 2021
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math9020178