Reciprocal Fibonacci constant

The Reciprocal Fibonacci Constant, or $\psi$, is defined as

$\psi =\sum _{k=1}^{\infty }{\frac {1}{F_{k}}}=3.359885666243177553172011\dots$

Not much is known about this constant except that is is irrational and transcendental , the problem of which was posed by Paul Erdos and proven by Richard André-Jeannin.