Liouville Number - Liouville Constant

Liouville Constant

The number

$c = \sum_{j=1}^\infty 10^{-j!} = 0.110001000000000000000001000\ldots$

is known as Liouville's constant. Liouville's constant is a Liouville number; if we define p_n and q_n as follows:

then we have for all positive integers n

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