Quantitative irrationality for sums of reciprocals of Fibonacci and Lucas numbers

Irrationality measures are given for the values of the series \(\sum_{n=0}^{\infty} t^{n}/W_{an+b}\), where \(a,b\in\mathbb{Z}^+, 1\le b\le a, (a,b)=1\) and Wn is a rational valued Fibonacci or Lucas form, satisfying a second order linear recurrence. In particular, we prove irrationality of all the numbers $$ \sum_{n=0}^\infty \frac{1}{f_{an+b}},\quad \sum_{n=0}^\infty \frac{1}{l_{an+b}}, $$ where fn and ln are the Fibonacci and Lucas numbers, respectively.