How fast must a continued-fraction-sequence increase that it is guaranteed to describe a Liouville-number?

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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

asked 2017-01-12

user id:82961

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I know that usually it is expected that the efforts are shown, but this time, I do not have any clue how to approach. – 2017-01-12
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http://math.stackexchange.com/questions/1668461/liouville-numbers-and-continued-fractions – 2017-01-12

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