The convergence Criteria ratio

[Amaelle]

Homework Statement

is the serie convergent or absolutely convergent?

Relevant Equations

The convergence Criteria ratio

Greetings all

I have a question regarding the convergence criteria ratio, abs(a_n+1/a_n) or the ⁿ√abs(a_n) when the limit tend to a value less than 1 does it mean the serie is convergent or absolutely convergent?

Thank you!

 

[FactChecker]

If the limit is less than 1, the series is absolutely convergent. It is only if the limit equals one that it might be convergent, but not absolutely convergent.

 

[Amaelle]

If the limit is less than 1, the series is absolutely convergent. It is only if the limit equals one that it might be convergent, but not absolutely convergent.

thank you!