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Math Help - convergence prob

  1. #1
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    convergence prob

    How do I determine if the following converges (using basic convergence tests: comparison, limit comparison, etc.)
    \sum\sin\frac{1}{n}
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by manyarrows View Post
    How do I determine if the following converges (using basic convergence tests: comparison, limit comparison, etc.)
    \sum\sin\frac{1}{n}
    Compare it to \sum\frac{1}{n}. Thus, it diverges.


    (See here for a similar problem.)
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  3. #3
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    Even on [1,infinity]

    It seems like it would converge since the sequence tends to zero and it is a decreasing and positive on this interval.
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  4. #4
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    Quote Originally Posted by manyarrows View Post
    Even on [1,infinity]

    It seems like it would converge since the sequence tends to zero and it is a decreasing and positive on this interval.
    You should read this: http://en.wikipedia.org/wiki/Harmoni...s_(mathematics)
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  5. #5
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    Quote Originally Posted by manyarrows View Post
    Even on [1,infinity]

    It seems like it would converge since the sequence tends to zero and it is a decreasing and positive on this interval.
    The series in question is not an alternating series.
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