Solving Inequality Problem with c1 to c2009

[thebluelagoon]

Homework Statement

Let c₁, c₂, c₃, …, c₂₀₀₉ be a sequence of real numbers such that |c_n – c_n+1| < 1 for 1 < n <2008. Show that:
| c₁+c₂+…+c₂₀₀₉ – c₁+c₂+…+c₂₀₀₈ |
|2009......2008...|< ½

Homework Equations

See above

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 |c_n - c_n+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!

 

[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.

 

[HallsofIvy]

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

 

[thebluelagoon]

2017036

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