Chapter 11.4, Problem 3E

(a) Use the Direct Comparison Test to show that the first series converges by comparing it to the second series. ${\displaystyle \underset{n=2}{\overset{\infty }{\sum }}\frac{n}{n^3+5}}{\displaystyle \underset{n=2}{\overset{\infty }{\sum }}\frac{1}{n^2}}$

(b) Use the Limit Comparison Test to show that that the first series converges by comparing it to the second series. ${\displaystyle \underset{n=2}{\overset{\infty }{\sum }}\frac{n}{n^3-5}}{\displaystyle \underset{n=2}{\overset{\infty }{\sum }}\frac{1}{n^2}}$