Is a Unit Step Function or Series the Solution to this Equation?

[the_dialogue]

Homework Statement

I have an equation that has the following values at different intervals:

It is:

r when 0<x<2Pi
r - (1)d when 2Pi<x<4Pi
r - (2)d when 4Pi<x<6Pi

And so on. I want to find a function that encompasses this whole function. Unit functions / discontinuity functions are fine; as long as I can take derivatives in the future.

2. The attempt at a solution

The furthest I could get is to define a series as follows:

r - n*d when 2nPi < x < 2(n+1)*Pi

At this point, my mind thinks discontinuity functions, but those would only work if 'n' was always a constant value, and didn't increase by 1 each iteration. Thank you!

 

[tim_lou]

cough, cough...the floor function.