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Proof by strong mathematical induction, can you see if this is enough to conclude?

  1. Oct 2, 2006 #1
    Hello everyone.

    THis is my first proof to strong mathematical induction so im' not sure if its correct or not it seems it though but then again I wrote it. Any suggestions/corrections would be great! THanks

    Here it is!
    [​IMG]
     
  2. jcsd
  3. Oct 3, 2006 #2

    Galileo

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    Your inductive hypothesis is that [tex]e_i\leq 3^i[/tex] for i=1,2,..,k-1, but you used:
    [tex]e_{k-1}\leq 3^k[/tex]
    [tex]e_{k-2}\leq 3^k[/tex]
    [tex]e_{k-3}\leq 3^k[/tex]

    That is certainly true, but not strong enough to conclude that
    [tex]e_{k}\leq 3^k[/tex]

    What if [tex]e_{k-1}=e_{k-2}=e_{k-3}= 3^k[/tex], then your three inequalities hold, but [itex]e_k=3^{k+1}[/itex]. You need to use your inductive hypothesis more strongly.
     
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