SUMS, PRODUCTS AND IDENTITIES INVOLVING k-FIBONACCI AND k-LUCAS SEQUENCES
http://dx.doi.org/10.17654/JPANTAFeb2014_063_077
In this paper, some basic properties of the k-Fibonacci and k-Lucas sequences are provided. Their relationship allows us to obtain some new properties involving sums and products of terms of these sequences. Furthermore, as a consequence of the Binet’s formula for each one, we also prove some identities involving these sequences.
Fibonacci numbers, Lucas numbers, k-Fibonacci numbers, k-Lucas numbers, Binet’s formula, recurrence relations.