# Laplace Transform

1. Oct 23, 2008

### 2RIP

1. The problem statement, all variables and given/known data
Is it possible to do the inverse laplace transform for this?

F(s) = $$\Sigma$$[e^(ns)]/s where n=0 and goes to infinity

2. Relevant equations
u_c(t) = [e^-(cs)]/s

3. The attempt at a solution

I don't think I can use this conversion because c or s is never less than 0... So is there another method to approach this problem?

2. Oct 23, 2008

### jeffreydk

Well I think, the sum converges,

$$\sum_{n=0}^{\infty}\frac{e^{ns}}{s}=\frac{-1}{(e^s-1)s}$$

So it will just be

$$-\mathcal{L}^{-1} \left\{ \frac{1}{(e^s-1)s} \right\}$$

3. Oct 23, 2008

### 2RIP

Oh, so there's no way to express it in terms of t? or even express [e^ns]/s in terms of t?

4. Oct 23, 2008

### jeffreydk

Well when you take the inverse laplace transform, in that last equation I wrote you will get it in terms of t. I was just showing you that the sum converges so you can simplify it.

$$f(t)=-\mathcal{L}^{-1} \left\{ \frac{1}{(e^s-1)s} \right\}$$

5. Oct 23, 2008

### 2RIP

Okay, I understand that. But I don't see any elementary laplace transform which has F(s) = e^s ... All of them has a negative sign in front of the s: e^-s. So i couldn't possibly set e^s/s = u_c(t)