I am not sure how to approach this infinite sum. I can see that it's a geometric series and that has a straightforward solution, but I am not sure how to address the alternating signs with the greatest integer function. Any ideas?
$\sum_{n=0} ^\infty (-1)^{\lfloor n/m \rfloor}r^n$, such that $0<r<1$ and $m \in N$.
We have $0<r<1$, so a general geometric series $\sum_{n=0} ^\infty ar^n$ will converge to $\frac{a}{1-r}$, but our $a$ here is $(-1)^{\lfloor n/m \rfloor}$.