Calculus (3rd Edition)

Published by W. H. Freeman

Chapter 11 - Infinite Series - 11.2 Summing and Infinite Series - Exercises - Page 547: 17

Diverges.

Work Step by Step

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.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.