The convergence Criteria ratio

Amaelle
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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(an+1/an) or the n√abs(an) when the limit tend to a value less than 1 does it mean the serie is convergent or absolutely convergent?

Thank you!
 
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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.
 
FactChecker said:
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!
 

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