MHB Which Test Should I Use: Ratio Test or Root Test in Series Convergence?

[aruwin]

Hello.
How do I determine whether to use ratio test or root test in determining whether a series is convergent or divergant? For example, in this problem, ratio is used for no.1 and root test for no.2. Why is that? I need explanation, please.

 

[Prove It]

Hello.
How do I determine whether to use ratio test or root test in determining whether a series is convergent or divergant? For example, in this problem, ratio is used for no.1 and root test for no.2. Why is that? I need explanation, please.

If your series has terms that will likely simplify with division (such as powers of n or factorials), then the ratio test is appropriate.

If your series will likely simplify by taking a root (e.g. because it has "n" in the power) then the root test is appropriate.

 

[aruwin]

If your series has terms that will likely simplify with division (such as powers of n or factorials), then the ratio test is appropriate.

If your series will likely simplify by taking a root (e.g. because it has "n" in the power) then the root test is appropriate.

Thank you!