Erdős 68: sharp factorial tail window $M!\sum_{n>M}\frac1{n!-1}\in\bigl(\frac1{M+1},\frac1M\bigr)$

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Erdős 68: sharp factorial tail window $M!\sum_{n>M}\frac1{n!-1}\in\bigl(\frac1{M+1},\frac1M\bigr)$ · Prove2Me