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Math Help - Convergence and Uniform Convergence

  1. #1
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    Convergence and Uniform Convergence

    Discuss the convergence ad the uniform convergence of the series \sum \frac {1} {n^2 x^2}.
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    Senior Member Shanks's Avatar
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    It converges whenever x is not 0.
    It uniformly converges in \{x:\left|x\right|>\delta\}\text{ for any }\delta >0
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  3. #3
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    Shanks,can you please further explain to me how to get the set for uniform convergence?
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  4. #4
    Senior Member Shanks's Avatar
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    \sum \frac{1}{n^2} = \frac{\pi^2}{6}
    Notice that if x approches 0, \frac{1}{n^2x^2} doesn't tend to 0.
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