An Interesting Problem Involving a Partition of $\mathbb{N}\setminus \left\lbrace 0\right\rbrace$

Suppose the positive integers are partitioned as $\left\{\left\{1\right\},\left\{2,3\right\},\left\{4,5,6\right\},\ldots\right\}.$ Call the elements of the partition $A_{n}$ where $A_{n}$ contains $n$ integers. Then, what is the sum of the integers in $A_{n}$? Call these sums $S_{n}.$ We can calculate a few sums … Continue reading →