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