scholarly journals On the Reciprocal Sums of Products of Balancing and Lucas-Balancing Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 350
Author(s):  
Younseok Choo
Keyword(s):  
Lucas Numbers ◽  
Balancing Numbers ◽  
Sums Of Products ◽  
Reciprocal Sums

Recently Panda et al. obtained some identities for the reciprocal sums of balancing and Lucas-balancing numbers. In this paper, we derive general identities related to reciprocal sums of products of two balancing numbers, products of two Lucas-balancing numbers and products of balancing and Lucas-balancing numbers. The method of this paper can also be applied to even-indexed and odd-indexed Fibonacci, Lucas, Pell and Pell–Lucas numbers.

scholarly journals On the reciprocal sums of products of Fibonacci and Lucas numbers

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2911-2920 ◽  
Author(s):  
Ginkyu Choi ◽  
Younseok Choo
Keyword(s):  
Lucas Numbers ◽  
Fibonacci And Lucas Numbers ◽  
Sums Of Products ◽  
Reciprocal Sums

In this paper, we study the reciprocal sums of products of Fibonacci and Lucas numbers. Some identities are obtained related to the numbers ??,k=n 1/FkLk+m and ??,k=n 1/LkFk+m, m ? 0.

On sums related to the numerator of generating functions for the kth power of Fibonacci numbers on sums related to the numerator of generating functions for the kth power of Fibonacci numbers

2010 ◽  
Vol 60 (6) ◽  
Author(s):  
Pavel Pražák ◽  
Pavel Trojovský
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Fibonacci Numbers ◽  
Similar Type ◽  
Lucas Numbers ◽  
Fibonomial Coefficients ◽  
Sums Of Products

AbstractNew results about some sums s n(k, l) of products of the Lucas numbers, which are of similar type as the sums in [SEIBERT, J.—TROJOVSK Ý, P.: On multiple sums of products of Lucas numbers, J. Integer Seq. 10 (2007), Article 07.4.5], and sums σ(k) = $$ \sum\limits_{l = 0}^{\tfrac{{k - 1}} {2}} {(_l^k )F_k - 2l^S n(k,l)} $$ are derived. These sums are related to the numerator of generating function for the kth powers of the Fibonacci numbers. s n(k, l) and σ(k) are expressed as the sum of the binomial and the Fibonomial coefficients. Proofs of these formulas are based on a special inverse formulas.

Irrationality results for reciprocal sums of certain Lucas numbers

1994 ◽  
Vol 62 (4) ◽  
pp. 300-305 ◽  
Author(s):  
Paul -Georg Becker ◽  
Thomas T�pfer
Keyword(s):  
Lucas Numbers ◽  
Reciprocal Sums
Sign in / Sign up

Export Citation Format

Share Document