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Math Help - Evaluating endpoints for conditionally or absolute convergence

  1. #1
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    Evaluating endpoints for conditionally or absolute convergence

    Q1)
    (x^n) / ((2^n)*ln(n)) = x is on the interval of -2 to 2. All of this is correct so far, however, I trouble evaluating the endpoints to see if they conditionally/absolute converges or diverges. According to the book answer, -2 conditionally converges, which I dont quite understand.

    My question is, how do I evaluate the endpoints for convergence/divergence? I plugged the numbers in, but dont quite grasp how to proceed from there.
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  2. #2
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    If S(x) = \sum\limits_n {\frac{{x^n }}{{2^n \ln (n)}}} then S(2) = \sum\limits_n {\frac{1}{{\ln (n)}}} clearly diverges.

    Whereas, S( - 2) = \sum\limits_n {\frac{{\left( { - 1} \right)^n }}{{\ln (n)}}} converges by the alternating series test.

    Does this help?
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  3. #3
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    Thank you! I understand it now.
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