Chapter 9.3, Problem 62E

a)

To determine

Find the series ${\displaystyle \sum _{n=2}^{\infty }\frac{1}{n\left(\ln n\right)}}$ converge or diverge using the result of Exercise 61.

b)

To determine

Find the series ${\displaystyle \sum _{n=2}^{\infty }\frac{1}{n{\left(\ln n\right)}^{1.01}}}$ converge or diverge using the result of Exercise 61.

c)

To determine

Find the series ${\displaystyle \sum _{n=2}^{\infty }\frac{1}{n\left(\ln n^3\right)}}$ converge or diverge using the result of Exercise 61.

d)

To determine

Find the series ${\displaystyle \sum _{n=2}^{\infty }\frac{1}{n{\left(\ln n\right)}^3}}$ converge or diverge using the result of Exercise 61.