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Mathematical Induction

  1. Jan 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Conjecture a simple formula for n = 2,4,6,8

    2. Relevant equations

    Kind of...
    [tex]Tn = (1-\frac{1}{n^2})(1-\frac{1}{(n-1)^2}).... to n=1[/tex]

    3. The attempt at a solution

    The pattern is 3/4, 5/8, 7/12, 9/16
    I know that the top is increasing by 2 and the bottom is increasing by 4... but I don't know how to put that into a formula to which I can prove.

    Thanks for any help!
    Last edited: Jan 25, 2009
  2. jcsd
  3. Jan 25, 2009 #2
    oooooh snap, how about this:

    [tex]Tn = \frac{n+1}{n*2}[/tex] for all even n?
  4. Jan 25, 2009 #3


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    Why not?
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