Answer
See below.
Work Step by Step
For any odd integer $n$, we can write $n=2k+1$ where $k$ is an integer.
We have:
$\lceil \frac{n}{2}\rceil =\lceil \frac{2k+1}{2}\rceil=\lceil k+\frac{1}{2}\rceil=k+1=\frac{n-1}{2}+1=\frac{n+1}{2}$
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