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Math Help - Is f continuous

  1. #1
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    Is f continuous

    Is the function given by \sum\limits_{n=1}^{\infty} (-1)^{n} \frac{\cos{nx}}{n^{3/2}} continuous for x \in [-\pi, \pi].
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  2. #2
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    Quote Originally Posted by Chandru1 View Post
    Is the function given by \sum\limits_{n=1}^{\infty} (-1)^{n} \frac{\cos{nx}}{n^{3/2}} continuous for x \in [-\pi, \pi].
    Since the series converges even absolutely for all x, this series defines a function that's even derivable everywhere.

    Tonio
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