MMN-1667
On the sum of reciprocal generalizedbi-periodic Fibonacci numbers
Abstract
The generalized Fibonacci sequence $\left\{q_{n}\right\}_{n=0}^{\infty}$ having initial conditions $q(0)=0$, $q(1)=1$ and recurrence relation $q_n=aq_{n-1}+q_{n-2}$ (when n is even and $n\geq2$) or $q_n=bq_{n-1}+q_{n-2}$
(when n is odd and $n\geq3$), where a and b are nonzero real numbers. Some well-known sequences, such as Fibonacci sequence, Pell’s sequence, the k-Fibonacci sequence, are special cases of this generalization.In this paper, we introduce the partial infinite sum of reciprocal generalized bi-periodic Fibonacci numbers.
Vol. 17 (2016), No. 1, pp. 35-41
DOI: 10.18514/MMN.2016.1667