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Homework Help: Series and sequences problem

  1. Jan 27, 2008 #1
    1. The problem statement, all variables and given/known data

    I need to find three mathematical series, for the following patterns

    1) Sn= 1/n if n is odd, or 1 of n is even.

    2) Sn= 0,1,0,.5,1,0,1/3,2/3,0,1/4........

    3) Find a sequence (Sk) which is a subset of the natural numbers in which every positive integer appears infinitely many times......that is, for each n in the Natural numbers, Sk=n for infinately many k's. any ideas???????????????????

    2. Relevant equations

    I guess they're arent any relevant equations to these. I guess yuo jsut have to get the pattern

    3. The attempt at a solution

    well, I know the first two are similar and thats about all I know. they're not p-series, geometric, alternating, or anything like that so I'm kind of stuck

    The third one, well, I don't even kow what it means honestly, so can you at least give me a hint?? thanks.
     
  2. jcsd
  3. Jan 27, 2008 #2
    For 1), try thinking along the lines of

    [tex]
    (-1)^n =
    \begin{cases}
    -1 & n\mbox{ is odd}\\
    1 & n\mbox{ is even}
    \end{cases}
    [/tex]

    For 2), try thinking along the lines of the periodicity of [tex]\sin(x)[/tex].

    For 3), I'll have to refer you to the Wikipedia article on "[URL [Broken] Paradox[/URL].
     
    Last edited by a moderator: May 3, 2017
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