Chapter 10.8, Problem 87E

a.

To determine

Whether the statement “If the Limit Comparison Test can be applied successfully to a given series with a certain comparison series, the Comparison Test also works with the same comparison series” is true or false.

b.

To determine

Whether the statement “The series ${\displaystyle \sum _{k=3}^{\infty }\frac{1}{k{\ln }^{p}k}}$ converges for the same values of p as the series ${\displaystyle \sum _{k=3}^{\infty }\frac{1}{k^p}}$” is true or false.

c.

To determine

Whether the statement “Both the Ratio Test and the Root Test can be applied conclusively to a geometric series” is true or false.

d.

To determine

Whether the statement “The Alternating Series Test can be used to show that some series diverge” is true or false.