## Calculus (3rd Edition)

Given $$\sum_{n=1}^{\infty} \frac{n}{10 n+12}$$ Since \begin{align*} \lim _{n \rightarrow \infty} \frac{n}{10 n+12}&=\lim _{n \rightarrow \infty}\left(\frac{1}{10+\frac{12}{n}}\right)\\ &=\frac{1}{10} \neq 0 \end{align*} Since the $n$th term $a_{n}$ does not converge to zero, thus the series diverges.