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A sequence $a_1,a_2,a_3,\cdots$ is given. Let $r$ be the number with continued fraction $[0,a_1,a_2,a_3,\cdots]$

How fast must the sequence increase that we can be sure that $r$ is a Liouville-number ?

For the definition of a Liouville-number, see here : http://mathworld.wolfram.com/LiouvilleNumber.html

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