we use two tests to see if a series is absolutely convergent, conditionally divergent or divergent?

Question

but usually what tests do we use, does the comparison test works most of the time, what about the 2nd test..im realli confused b/t what tests...could u plz help me out? thanks!

Answer 1

The limit 0 is a necessary but by no means sufficient condition for convergence.
It depends on the series what test to use
Each case can be different.
post examples.

Answer 2

you can always take the limit at the function as x->infinity and see if you get zero, which shows that it converges.