Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A function is defined by
Find . At which values of does the graph have a jump?
means . is the greatest integer not above , and lies in . A piecewise function uses the rule for the piece that holds the input.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The values. , , , , . The sum is .
Step 2. At . From the left, approaches , but : a jump.
Step 3. At . and : no jump.
Answer: the sum is ; the only jump is at .
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