What is the exact (closed form) value of the expression, where $f_1=f_2=1$ and $f_{n+1}=f_n+f_{n-1}\forall n\ge 2$,$$\dfrac{1}{f_1}+\dfrac{1}{f_1f_2}+\dfrac{1}{f_1f_2f_3}+\cdots+\dfrac{1}{f_1f_2\cdots f_{\ell}}+\cdots$$ I approximate it by computer that it is about $1.74\dots$ and we know that it is irrational but I don't know how to find its closed form.
I interest this because it is involving the Fiboncci sequences but I haven't seen anything like this that I googled. So it maybe not of interest to others so I would also know (the following dumb questions) that. Why doesn't this one be studied or why does it not be interested?