# Having a hard time understanding this

1. Nov 11, 2012

### Zondrina

This question was posted in the homework forum. To my understanding, this looks like two different questions as the first hypothesis is not true due to a simple counter-example argument. The second one would be true by two induction arguments on k>2 and k<0.

Am I wrong in thinking this? It seems logical since he said "there exists a c >1" so I would figure any REAL c must make the inequality true?

Last edited: Nov 11, 2012
2. Nov 11, 2012

### Arkuski

I would use induction on this. The wording is pretty awkward and it seems like two different questions but I think they are looking for an induction type proof.

3. Nov 11, 2012

### LeonhardEuler

Zondrina, I had the same confusion as you when I first read the question. It is actually only one question. The first part is not saying
" if m>1 then there exists a c>1 that satisfies
cm<mc"
The whole thing is saying that if the number "m" is such that some "c" exists satisfying the requirement, then every k>c satisfies the second inequality.

4. Nov 11, 2012

### Zondrina

Yes this makes sense now, thank you. If that were the case though, would I have been wrong to say that?

I thought he meant for every m>1, there exists a c>1 which satisfies .. blah.