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Math Help - Uniform boundedness

  1. #1
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    Uniform boundedness

    Prove that the partial sums of \sum cos nx are uniformly bounded. Note: Sorry I don't know laytex .

    Attempt:

    n/m, I've solved it.
    Last edited by skepticsmind; December 16th 2009 at 02:54 PM.
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  2. #2
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    Quote Originally Posted by skepticsmind View Post
    Prove that the partial sums of \sum cos nx are uniformly bounded. Note: Sorry I don't know laytex .

    Attempt:

    n/m, I've solved it.
    Is this really unif. bounded? In which interval? If you work in \mathbb{R} then taking x=2\pi we get that \sum \cos (nx) = \sum 1 = \infty so it can't be unif. (not even pointwise) bounded in the whole line.
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