3.23: Well, if an integer $n > 1$, it actually means $n \ge 2$, right?

3.24: Telescoping means you split each term into two terms, and then adjacent terms cancel out. More details in class.

3.25: You actually said it pretty well.  Just give it a little bit more thought, you will know why the paired terms add up to 100 (hint: you already know that, without the floor function, the terms add up to 101.  Then what happens if you take the floor of each? Remember the floor function results in integers.).

3.26: For smaller numbers, each value of obtained multiple times, so the values 0, 1, 2, ..., are all taken, up to a certain value.  Up to this point, we know each of the consecutive numbers have appeared, so we know how many they are.  Once this certain value is reached, the values after it will not be consecutive, but each value only appears once, so we can count by counting the terms. Combining these two steps, you can get the total number of possible values.