Inverse Laplace Transform of exponential

Question

Is it possible to compute the inverse Laplace transform of: $$\frac{1}{1-e^{-sa}}$$ where $a>0$ ?

Answer 1

A possible solution is as follows.

$$\left( 1-{{\rm e}^{-sa}} \right) ^{-1}=\sum _{n=0}^{\infty } \left( {{\rm e}^{-sa}} \right) ^{n} $$

Now, the inverse laplace transform of $e^{-nsa}$ is $Dirac(t-an)$.

Then we have

$$\sum _{n=0}^{\infty }{\it Dirac} \left( t-an \right) $$ Do you agree?