Convergent of sequence looking like Riemann zeta function I have a question that: Given a non-negative sequence {$\epsilon_n$} ($n \in \mathbb{Z+}$) such that $\lim_{n \rightarrow +\infty}\epsilon_n = 0$.
Can we conclude that $\sum_{n \in \mathbb{Z+}}\frac{\epsilon_n}{n} < +\infty$

Not sure what this has to do with zeta functions. The answer is no: take $\epsilon_n=1/\ln(n+1)$. Use the integral test to show the series diverges.
