01.Answer

Here are a few properties:

• The sum of the empty list is 0 -- sum(Nil) == 0.
• The sum of a list whose elements are all equal to x is the list's size multiplied by x -- sum(List.fill(n)(x)) == n * x.
• For any list xs, its sum is equal to the sum of xs.reverse -- sum(xs) == sum(xs.reverse). This follows from the fact that addition is commutative.
• For any list xs, partitioning it in to two lists, summing each partitioning, and then adding the sums yields same result as summing xs. This follows from the fact that addition is associative.
• The sum of the list with elements 1, 2, 3...n is n*(n+1)/2.