Help me calculate the Laplace transform of a geometric series. $$ f(t) = \sum_{n=0}^\infty(-1)^nu(t-n) $$
show that $$ \mathcal{L} \{f(t)\} = \frac{1}{s(1+\mathcal{e}^{-s})} $$
Edit: so far I know that
$$ \mathcal{L} \{f(t)\} = \frac{1}{s}\sum_{n=0}^\infty(-1)^ne^{-ns} $$