# Homework Help: Inequality problem

1. Sep 30, 2008

### thebluelagoon

1. The problem statement, all variables and given/known data
Let c1, c2, c3, …, c2009 be a sequence of real numbers such that |cn – cn+1| < 1 for 1 < n <2008. Show that:
| c1+c2+…+c2009 c1+c2+…+c2008 |
|2009............................2008...............|< ½

2. Relevant equations

See above

3. The attempt at a solution

Well I simplified by cross-multiplying, getting
2008(c1 + c2 + ... + c2009) - 2009(c1 + c2 + ... + c2008)

Which thus gives us
-c1 - c2 - ... - c2008 + 2008c2009

I want to use |cn - cn+1| < 1 but I then noticed that's only for 1<n<2008 (is this a parameter that'll affect us?) and then also that bracketing gives us

-(c1+c2+...+c2008 - 2008c2009).

I just don't know the next step now. Any pointers would be appreciated!

2. Oct 1, 2008

### thebluelagoon

Um, can no-one help me? I'm sure it's not that hard, I'm just missing the next step. Sorry to bump it, but it really is bugging me.

3. Oct 1, 2008

### HallsofIvy

You have completely left out the right side of your inequality. What will that be after "cross multiplying"?

4. Oct 1, 2008

### thebluelagoon

2017036

so could we then change it to -c-c2-...-c2008 <2017036 - 2008c2009
and dow something with that?