Let $\beta = \sum _ { n = 1 } ^ { + \infty } \frac { 1 } { 10 ^ { n ! } }$. Justify that $\beta$ is well-defined, then show that $\beta$ is an irrational number.
Let $\beta = \sum _ { n = 1 } ^ { + \infty } \frac { 1 } { 10 ^ { n ! } }$.
Justify that $\beta$ is well-defined, then show that $\beta$ is an irrational number.