MathDB
G 26

Source:

May 25, 2007
Irrational numbers

Problem Statement

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.
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