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.