Some addition formulas for Fibonacci, Pell and Jacobsthal numbers - Bilgici, Göksal; Şentürk, Tuncay Deniz (Annales Mathematicae Silesianae, 2019)
In this paper, we obtain a closed form for FΣ_{i=1}^k, PΣ_{i=1}^k and JΣ_{i=1}^k for some positive integers k where Fr, Pr and Jr are the rth Fibonacci, Pell and Jacobsthal numbers, respectively. We also give three open problems for the general cases FΣ_{i=1}^n, PΣ_{i=1}^n and JΣ_{i=1}^n for any arbitrary positive integer n.