# Is it possible to compute the inverse Laplace transform of: (1)/(1-e^(-sa)) where a>0 ?

Is it possible to compute the inverse Laplace transform of:
$\frac{1}{1-{e}^{-sa}}$
where a>0 ?
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canhaulatlt
A possible solution is as follows.
${\left(1-{\mathrm{e}}^{-sa}\right)}^{-1}=\sum _{n=0}^{\mathrm{\infty }}{\left({\mathrm{e}}^{-sa}\right)}^{n}$
Now, the inverse laplace transform of ${e}^{-nsa}$ is $Dirac\left(t-an\right)$
Then we have
$\sum _{n=0}^{\mathrm{\infty }}\mathit{D}\mathit{i}\mathit{r}\mathit{a}\mathit{c}\left(t-an\right)$