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Math Help - How is problem 4 done?

  1. #1
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    How is problem 4 done?

    If you could just help me out with problem 4 here, that would be great. Thanks

    http://math.rutgers.edu/~jsosa/Courses/Math152/w10.pdf
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  2. #2
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    Quote Originally Posted by zhupolongjoe View Post
    If you could just help me out with problem 4 here, that would be great. Thanks

    http://math.rutgers.edu/~jsosa/Courses/Math152/w10.pdf
    For 1., we can test for ABSOLUTE convergence.

    So if \sum_{n = 2}^\infty{\frac{1}{n(\ln{n})^2}} converges, so does \sum_{n = 2}^\infty{\frac{(-1)^n}{n(\ln{n})^2}}.

    Notice that \int_2^\infty{\frac{1}{x(\ln{x})^2}\,dx} is a relatively easy integral to solve (just use a u-substitution). So you could do an integral test.

    Edit: Should have read your original post more carefully - you've already done this one
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