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Math Help - subsequence

  1. #1
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    subsequence

    show that (sin(n)) with n in N.

    Hint: Find a subsequence each of whose terms in is [1/2,1] and another subsequence each of whose terms is in [-1,-1/2].
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  2. #2
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    Quote Originally Posted by Jdg6057 View Post
    show that (sin(n)) with n in N.

    Hint: Find a subsequence each of whose terms in is [1/2,1] and another subsequence each of whose terms is in [-1,-1/2].

    Show what? Apparently that it diverges:

    Take {sin(nPi/2), with n odd numbers = 1 (mod 4), so n = 1,5,9,13,17,...etc.. This subsequence is all 1's

    Take now sin(nPi/2) with n odd = 3 (mod 4), i.e. n = 3,7,11,15, etc.
    This subsequence is all -1's.

    Tonio
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