CPM Homework Help : CALC Problem 10-89

Determine if the following series converge or diverge. State the test you used. Homework Help ✎

Hint (a):

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

Hint (b):

Use the Ratio Test.

Hint (c):

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

Hint (d):

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

More Help (d):

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

Hint (e):

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

Hint (f):

Use the Limit Comparison Test with 1/n⁴.