First, let's figure out the pattern that this series follows. We can see that the first number is increased by 1/2 to get to 2 1/2. Then, the second number is decreased by 1 to get to 1 1/2. Finally, the pattern repeats.
So, let's apply this pattern to find the next number in this series.
2, 2 1/2, 1 1/2, 2, 1
The next number in this series is 1.
Hope this helps!! :)