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Convergence of series, sequences and functions and different modes of convergence.

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The growth of a sequence related to Liouville numbers [closed]

I am doing a work on Liouville numbers. The Liouville constant $\ell=\sum_{k\geq 0}10^{-k!}$ has its approximation by rational numbers related to the fact that for $v_n=n!$, then $v_{n+1}/v_n$ tends t …
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