K. M. Nagaraja and P. Dhanya

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 26, 2020, Number 3, Pages 189–202

DOI: 10.7546/nntdm.2020.26.3.189-202

**Full paper (PDF, 205 Kb)**

## Details

### Authors and affiliations

K. M. Nagaraja

*Department of Mathematics, J.S.S. Academy of Technical Education
Uttarahalli-Kengeri Main Road, Bengaluru-60, Karnataka, India
*

P. Dhanya

*Department of Mathematics, J.S.S. Academy of Technical Education
Uttarahalli-Kengeri Main Road, Bengaluru-60, Karnataka, India*

### Abstract

In this article, the concepts of Fibonacci, Tribonacci, Lucas and Tetranacci numbers are generalized as continued sum. The generalized Fibonacci identity is proved by using induction and the binomial theorem. Further, it is proved that the generalized Fibonacci and Lucas sequences are logarithmically convex (concave) and some special identities are obtained.

### Keywords

- Sequence
- Fibonacci number
- Lucas number
- Tribonacci number
- Golden ratio

### 2010 Mathematics Subject Classification

- 11B39

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## Cite this paper

Nagaraja, K. M., & Dhanya, P. (2020). Identities on generalized Fibonacci and Lucas numbers. *Notes on Number Theory and Discrete Mathematics*, 26 (3), 189-202, DOI: 10.7546/nntdm.2020.26.3.189-202.