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Let $d;n$ mean repeat the digit $d$, $n$ times. Let $|$ be a digitwise concatenation, such that $2|34|6=2346$ This allows constants to be created for example \begin{equation}  \lim_{n\to\infty} C=\lim_{n\to\infty}  \frac{1|3;n|8}{2|8;n|7} \end{equation} For a given sequence it is not entirely clear if convergence will be achieved. We may take a partial series. For $n=24$ we have $C=0.461538461538461538461538653254437869822485207100604251251706...$ which appears to repeat at first with a $6$ digit sequence $.461538$.