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xnx show tha Outlet XnER be such that Ixi De Ynt X IR and llaurillth 1 Xull 1 Vua loo 3pts . letxuE co prove or disprove that {xn is abs. Cour. и

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.

Learn more about absolute convergence of a sequence here:

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