Solution to Elementary Analysis: The Theory of Calculus Second Edition Section 7 Exercise 7.2

Solution:

(a) Converges. Limits is 0.

(b) Converges. Limits is $3/4$. See Example 2,

$$

\frac{3n+1}{4n-1}=\frac{3+\frac{1}{n}}{4-\frac{1}{n}}.

$$

(c) Converges. Limits is 0.

(d) Diverges. (Indeed, it is periodic.)