How do we prove that:

 

[math](1+x)^h<1 +xh [/math] ,where : 0<h<1 and [math]x\neq 0[/math] x>-1

Edited April 8, 201015 yr by triclino
correction

As stated, this is wrong. What happens at x=0?

 

Eliminate that particular value for x and the statement is true. This suggests a route by which you can prove this conjecture: Split the proof into two parts, one for[math]x\,\in(-1,0)[/math] and the other for [math]x>0[/math].

This suggests a route by which you can prove this conjecture: Split the proof into two parts, one for[math]x\,\in(-1,0)[/math] and the other for [math]x>0[/math].

 

This suggests nothing ,because you do not say what must we do in those two parts

THis looks like homework, triclino. We don't do your homework for you. We do give hints.

THis looks like homework, triclino. We don't do your homework for you. We do give hints.

 

This is not homework .This a problem i would like to investigate and i bring it to the attention of the forum and wait for any suggestions .

 

On the other hand you can baptise every problem as home work and give irrelevant hints ,since you will not pursue the problem any further because it is homework

This is an easy problem, triclino. I generally solve a problem on which I offer assistance before I offer assistance -- this one included.

I do not understand ,why you give irrelevant hints ,if you already know the problem.

 

Sometimes an easy problem has deeper consequences and we need to investigate.

 

Also every problem has various levels of proofs and according to what kind of proof we are asked to produce a very easy problem can become extremely difficult

triclino, the hint is not irrelevant. In fact it is a key step in the proof - the first step, in fact. Please refer to my other post regarding your behaviour.