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Math Help - alternating series #2

  1. #1
    Senior Member mollymcf2009's Avatar
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    alternating series #2

    \sum^{\infty}_{n=1} (-1) sin(\frac{6\pi}{n})

    Would I compare this to sin\frac{1}{n}?
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  2. #2
    MHF Contributor matheagle's Avatar
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    Is this alternating or can we pull out the negative one?

    Do a limit comp to the harmonic series, which diverges. Then use let m=1/n and use

    {\sin m\over m} goes to one as m\to 0.
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  3. #3
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by matheagle View Post
    is this alternating or can we pull out the negative one?
    Are you asking me? This is in the alternating series section of my homework. I think that I can pull it out.
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  4. #4
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    Are you asking me? This is in the alternating series section of my homework. I think that I can pull it out.
    yes, do you mean (-1) or (-1)^n
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  5. #5
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by matheagle View Post
    Is this alternating or can we pull out the negative one?

    Do a limit comp to the harmonic series, which diverges. Then use let m=1/n and use

    {\sin m\over m} goes to one as m\to 0.
    But I don't understand why you did that? Why does sin(m)/m go to 1 as m goes to 0?
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  6. #6
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by matheagle View Post
    yes, do you mean (-1) or (-1)^n
    It is (-1)^n so since there is an n as an exponent I CAN'T pull it out? I am CONFUSED!!!!!
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  7. #7
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    But I don't understand why you did that? Why does sin(m)/m go to 1 as m goes to 0?
    basic calculus one, or use l'hopital's rule
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