On the Reciprocal Sums of Products of Two Generalized Bi-Periodic Fibonacci Numbers
This paper concerns the properties of the generalized bi-periodic Fibonacci numbers {Gn} generated from the recurrence relation: Gn=aGn−1+Gn−2 (n is even) or Gn=bGn−1+Gn−2 (n is odd). We derive general identities for the reciprocal sums of products of two generalized bi-periodic Fibonacci numbers. More precisely, we obtain formulas for the integer parts of the numbers ∑k=n∞(a/b)ξ(k+1)GkGk+m−1,m=0,2,4,⋯, and ∑k=n∞1GkGk+m−1,m=1,3,5,⋯.
2019 ◽
Vol 13
(12)
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pp. 539-549
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1997 ◽
Vol 73
(7)
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pp. 140-142
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2019 ◽
Vol 110
(2)
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pp. 321-333