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Show by induction that (1-nu)(1+u)<=1 for n=0,1,2,3 and u>-1

  1. Oct 29, 2011 #1
    Hi, I have to solve this problem... I have done something, but I don't know if it is right :/ Thanks a lot for your help!

    "Show by induction that (1-nu)(1+u)<=1 for n=0,1,2,3... and u>-1"

    For n=0:
    (1-0*u)(1+u)^0 <=1
    1*1<=1
    1<=1, which is true.

    Assume that the statement is true for n=k: (1-ku)(1+u)^k<=1

    Then it follows that

    (1-(k+1)u)(1+u)^(k+1) <= 1... And how do I continue? I really don't have a clue what to do now :(
     
  2. jcsd
  3. Oct 31, 2011 #2

    mathman

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    (1-(k+1)u)(1+u)/(1-ku)

    Is this expression <=1?
     
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