Consider the function $$\begin{cases} \displaystyle\sum_{r=0}^{2\mu}f(r)(-1)^r\qquad \text{for even $\mu$}\\ \displaystyle\sum_{r=0}^{2\mu}f(r)(-1)^{r+1}\qquad \text{for odd $\mu$}\\\end{cases}$$
Is there a neat notation where the two expressions can be combined into one which will automatically cater for both even and odd values of $\mu$ without splitting into two cases?
$$\sum_{r=0}^{2\mu}f(r)(-1)^{r+\mu}$$