How do we show that if $g \geq 2$ is an integer, then the two series $\sum\limits_{n=0}^{\infty} \frac{1}{g^{n^{2}}} \quad \ \text{and} \ \sum\limits_{n=0}^{\infty} \frac{1}{g^{n!}}$ both converge to irrational numbers.
Well, i tried to see what happens, if they converge to a rational but couldn't get anything out it.