Compute the Laplace Transforms of th following three unrelated functions:

$f\_1(t)=\sum\_{n=0}^\infty (-1)^n u(t-n)$ 

where $u(t-n)$ is the usual step function

$f\_2(t)=\sum\_{n=0}^\infty u(t-n)$

$f\_3(t)=t - \left\lfloor t \right\rfloor$

where $t>0$ and $\left\lfloor t \right\rfloor$ is the floor function of $t$ and $u(t-n)$ is the usual step function.

I assume that I would just have to evaluate the sums and then take the Laplace Transform as usual, right? But if that were the case, wouldn't the two sums just converge to zero?