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Lost on why he used 2.7 rather than 1.7, typo perhaps?

  1. Oct 16, 2006 #1
    Hello everyone i'm revewing a proof by strong mathematical induction and it seems to be making sense all the way up to this point:
    Since (1.7)^2 = 2.98 > 2.7, we have...

    WHy did he compare 1.7^2 > 2.7? we've been using 1.7 the whole time.


  2. jcsd
  3. Oct 16, 2006 #2
    The 2.7 comes about because he factors out [itex](1.7)^{k-2}[/itex] from the following expression

    (1.7)^{k-1} + (1.7)^{k-2} = (1.7)^{k-2}\left(1.7 + 1\right) = (1.7)^{k-2}(2.7)

    i.e. [itex]1.7 + 1 = 2.7[/itex]. He wants to make this statement about [itex](1.7)^2>2.7[/itex] so he can use it in the proof. Notice that in the penultimate step he uses an inequality (which assumes the above condition).
  4. Oct 16, 2006 #3
    Ahh i c it now, thank u for the help!
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