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Math Help - alternating series help

  1. #1
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    alternating series help

    is the following series an alternating series?

    Sum n=1, inf, cos(npi)/n^2

    can i write it as Sum n=1,inf, ((-1)^(n-1))/n^2, then use the alternating series test, and put it in absoulte value and get 1/n^2 which is a convergent p series? is this correct? thanks
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by andrewt328 View Post
    is the following series an alternating series?

    Sum n=1, inf, cos(npi)/n^2

    can i write it as Sum n=1,inf, ((-1)^(n-1))/n^2, then use the alternating series test, and put it in absoulte value and get 1/n^2 which is a convergent p series? is this correct? thanks
    Yes, Sum n=1, inf, cos(npi)/n^2 is an alternating series.
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  3. #3
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    and it will converge since its a p-seires, and that means that the original series will converge? thanks
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by andrewt328 View Post
    and it will converge since its a p-seires, and that means that the original series will converge? thanks
    correct!
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  5. #5
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    awsome, thanks for the help!!
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