ThmDex – An index of mathematical definitions, results, and conjectures.
Standard real harmonic series diverges
Formulation 0
Let $x_1, x_2, x_3, \ldots \in \mathbb{Q}$ each be a D994: Rational number such that
(i) \begin{equation} x_n = \frac{1}{n} \end{equation}
Then \begin{equation} \sum_{n = 1}^{\infty} x_n = \infty \end{equation}
Formulation 1
Let $x_1, x_2, x_3, \ldots \in \mathbb{Q}$ each be a D994: Rational number such that
(i) \begin{equation} x_n = \frac{1}{n} \end{equation}
Then \begin{equation} \lim_{N \to \infty} \sum_{n = 1}^N x_n = \infty \end{equation}