### Home > CALC > Chapter 10 > Lesson 10.2.1 > Problem10-89

10-89.

$\text{Is }\lim_{n\to\infty}\frac{n}{2n+5}=0?$

Use the Ratio Test.

$\text{Is }\lim_{n\to\infty}\ln\Big(\frac{1}{n}\Big)=0?$

$\left|\cos(n)\right|\le1$

$\frac{\cos(n)}{2^n}\le\frac{1}{2^n}$

This is a geometric series. What is the value of r?

Use the Limit Comparison Test with 1/n4.