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

[gilabert1985]

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 :(

 

[mathman]

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

Is this expression <=1?