MathDB

26

Part of PEN G Problems

Problems(1)

G 26

Source:

5/25/2007
Prove that if g≥2g \ge 2 is an integer, then two series ∑n=0∞1gn2    and    ∑n=0∞1gn!\sum_{n=0}^{\infty}\frac{1}{g^{n^{2}}}\;\; \text{and}\;\; \sum_{n=0}^{\infty}\frac{1}{g^{n!}} both converge to irrational numbers.
Irrational numbers