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Math Help - Testing for Convergence of (Trigonometric) Series

  1. #1
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    Testing for Convergence of (Trigonometric) Series

    Hello, and thanks in advance for the help.

    I need to test for whether or not the following series converges:

    Sum (from 1 to infinity) of sin(1/(n^2))

    The only partial solution I can think of is that the max of the sine function is 1 and the minimum is 0 if you take the absolute value...but I'm not sure how to translate this into anything useful.

    Thanks again guys...this forum is a great utility.
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  2. #2
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    Quote Originally Posted by NBrunk View Post
    Hello, and thanks in advance for the help.

    I need to test for whether or not the following series converges:

    Sum (from 1 to infinity) of sin(1/(n^2))

    The only partial solution I can think of is that the max of the sine function is 1 and the minimum is 0 if you take the absolute value...but I'm not sure how to translate this into anything useful.

    Thanks again guys...this forum is a great utility.

    Hints: 1) the series is a positive one
    2) For x > 0 close enough to zero, \sin x < x

    Tonio
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  3. #3
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    Use the integral test.
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  4. #4
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    Use the limit comparison test with the convergent series \sum_{n \geq 1} \frac{1}{n^2} ..
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