Inverse Laplace Transform for F(s): Is it Possible?

[2RIP]

Homework Statement

Is it possible to do the inverse laplace transform for this?

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

Homework Equations

u_c(t) = [e^-(cs)]/s

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?

Thank you in advance.

 

[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

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

 

[2RIP]

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

 

[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.

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

 

[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)