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Math Help - Does the following series have a majorant series?

  1. #1
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    Does the following series have a majorant series?

    A majorant series is a series that is equal or larger.
    The series \sum^{\infty}_{n=1}k_n is a majorant series to \sum^{\infty}_{n=1}f_n(x) if:
    |f_n(x)|\leq k_n

    Does the following series have a majorant series?


    I'm not sure what arguments to use here. Cosine's maximum value can only be 1 but how do I find a series that can be equal to or larger than this?
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  2. #2
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    Re: Does the following series have a majorant series?

    How about \sum_{n=0}^\infty 1.
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    Re: Does the following series have a majorant series?

    Quote Originally Posted by HallsofIvy View Post
    How about \sum_{n=0}^\infty 1.
    Yes, that is true.
    my next question is whether or not a convergent majorant series exist? It doesn't seem like such a series exists?
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