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Math Help - series convergent or divergent?

  1. #1
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    series convergent or divergent?

    Could someone help me show the convergence/divergenceof the following (without the Dirichlet test or Abel sum test)?

    sum(cos(n)/n) from n=1 to inf

    I cannot use the comparison test since cos(n) alternates and our prof. does not want us to use Dirichlet test. Could someone please help?

    Thanks!
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by sdh2106 View Post
    Could someone help me show the convergence/divergenceof the following (without the Dirichlet test or Abel sum test)?

    sum(cos(n)/n) from n=1 to inf

    I cannot use the comparison test since cos(n) alternates and our prof. does not want us to use Dirichlet test. Could someone please help?

    Thanks!
    If you're doing this rigorously I would note that if \displaystyle s_m=\sum_{n=1}^{m}\frac{\cos(n)}{n} then \displaystyle s_m=\text{Re}\sum_{n=1}^{m}\frac{e^{in}}{n} and go from there.
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    the op asked for convergence proof, not for sum value.
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