- #1

kostoglotov

- 234

- 6

1. Homework Statement

1. Homework Statement

Unit stair-case function: [itex]f(t) = n, \ if \ \ n-1 \leq t < n, \ \ n = 1,2,3,...[/itex]

Show that [itex]f(t) = \sum_{n=0}^{\infty} u(t-n) \ [/itex] for all [itex]t \geq 0[/itex]

## Homework Equations

## The Attempt at a Solution

I can see how as we move through the values of n, each unit step function will just be adding one, which just builds the stair-case, but after any given t is reached, won't that sum just keeping adding an infinite number of 1's to result?

Does the sum to infinity actually stop at some finite point because [itex]n-1 \leq t < n, \ \ n = 1,2,3,...[/itex]? Wouldn't that contradict the idea of having an infinite sum?

Or does the unit step function used in the sum drop down to zero after a certain n is reached? How would that work?