Problem 9
Consider the sequence of sets with the following properties:
- Each set contains only consecutive integers.
- The nth set has one more element than the (n-1)th set.
- The least element of the nth set is one more than the greatest element in the (n-1)th set.
- The first set is {1}.
In other words, consider the sets {1}, {2,3}, {4,5,6}, {7,8,9,10}, ...
Now let
S(
n) be the sum of the elements in the
nth set.
Find a formula in terms of
n for
S(
n).
