- #1
gilabert1985
- 7
- 0
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 :(
"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 :(
