2. Consider the list {1,2, ..., n}, where n is a positive integer.

a) Guess the average of the list and give an intuitive explanation for your guess.

b) Prove that your guess in part a is correct.

c) Let i be an element of the list; in other words, suppose i is an integer such that 1 i n.

Suppose the element i gets replaced by 0. By how much does the average change? If you

followed what we did in class, you should be able to just write down this answer and

explain it without calculation.

d) Start with the original list {1,2,...,n} and delete an element i. What is the average of the

new list?