Let g ∈ N {\displaystyle {}g\in \mathbb {N} } , g ≥ 2 {\displaystyle {}g\geq 2} . A sequence of digits, given by
(where k ∈ N {\displaystyle {}k\in \mathbb {N} } ) defines a real series
Prove that such a series converges to a unique non-negative real number.