Determine if is absolutely convergent, conditionally convergent or divergent.
A) absolutely convergent
B) conditionally convergent
C) divergent

Question

Determine if  is absolutely convergent, conditionally convergent or divergent.
A) absolutely convergent 
B) conditionally convergent 
C) divergent

Quizplus · Accepted Answer

To determine the convergence of the given series, we need to apply the alternating series test. The alternating series test states that if a series satisfies the following conditions:
1. The series alternates in sign
2. The absolute value of the terms decreases
3. The limit of the absolute value of the terms approaches zero
then the series is convergent.

In the given series, we can see that the terms alternate in sign and the absolute value of the terms is decreasing. Moreover, the limit of the absolute value of the terms approaches zero as n approaches infinity.

Therefore, the given series is absolutely convergent.

Determine If Is Absolutely Convergent, Conditionally Convergent or Divergent