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Proof by Induction - Inequalities

  1. Oct 7, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove by induction that: (Please see attachment)

    2. Relevant equations

    3. The attempt at a solution

    Can someone please confirm if I have worked the question out correctly. Many thanks.
     

    Attached Files:

  2. jcsd
  3. Oct 7, 2011 #2

    ehild

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    Your method is not correct. Start from the inequality you supposed to be true (for n=k) and transform it till you arrive to the desired form. You started from the case n=k+1 and went backwards. That is wrong.


    ehild
     
  4. Oct 7, 2011 #3

    HallsofIvy

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    It might help you to note that
    [tex]\frac{1}{(1+r)^n}\le \frac{1}{1+ rn}[/tex]
    is exactly the same as
    [tex]1+ rn\le (1+ r)^n[/tex]
    so you don't have to worry about the fractions.
     
  5. Oct 7, 2011 #4
    the second line from the end looks incorrect.
    [itex]\frac{1}{k\cdot r^2} \le 0 \Leftrightarrow k<0, r\ne 0[/itex]
    why won't you try to attack it from another aspect. for example,
    [itex]p_1>p2>0 \rightarrow \frac{1}{p_2}>\frac{1}{p_1}[/itex]
     
  6. Oct 7, 2011 #5
    Thank you for the help guys. I genuinely appreciate it.
     
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