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

  • #1

Main Question or Discussion Point

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 :(
 

Answers and Replies

  • #2
mathman
Science Advisor
7,771
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(1-(k+1)u)(1+u)/(1-ku)

Is this expression <=1?
 

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