Irrational number
Posted: Fri Mar 25, 2016 8:31 am
$\newcommand{\lcm}{{\rm lcm}}$ Let $\lcm$ denote the least common divisor. Prove that the number:
$$\mathcal{I}=\sum_{n=1}^{\infty} \frac{1}{\lcm (1, 2, \dots, n)}$$
is irrational.
$$\mathcal{I}=\sum_{n=1}^{\infty} \frac{1}{\lcm (1, 2, \dots, n)}$$
is irrational.