Answer :
Final answer:
To prove or disprove that {xn is absolutely convergent}, we need to determine whether the series formed by taking the absolute values of the terms converges or diverges. Apply the appropriate convergence test to the series |xn| to determine its convergence or divergence. Based on the result, we can conclude whether the sequence {xn} is absolutely convergent or not.
Explanation:
To prove or disprove that {xn is absolutely convergent}, we need to determine whether the series formed by taking the absolute values of the terms converges or diverges.
Let's consider the given sequence {xn} and its corresponding series |xn|.
If the series |xn| converges, then the sequence {xn} is absolutely convergent. On the other hand, if the series |xn| diverges, then the sequence {xn} is not absolutely convergent.
To determine the convergence or divergence of the series |xn|, we can use convergence tests such as the Comparison Test, Ratio Test, or Root Test.
Apply the appropriate convergence test to the series |xn| to determine its convergence or divergence. Based on the result, we can conclude whether the sequence {xn} is absolutely convergent or not.
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