Thanks for stopping by to look at my question.
I'm trying to show that $R$ is irrational in $$R:= \dfrac{1}{F_1}+\dfrac{1}{F_2\cdot F_1}+\dfrac{1}{F_3\cdot F_2 \cdot F_1}+\dfrac{1}{F_4\cdot F_3\cdot F_2 \cdot F_1}+\cdots$$ where $F_n$ are the Fibonacci numbers and $R<3$ and $F_{n+k}>F_k$ for $n>0$.
How should I approach this? Where is this series from?