In the infinite series 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5... each positive integer k appears k times in consecutive order.

Write a formula for the sum of the first n terms of the series.

(In reply to re(2): A formula by Dej Mar)

The infinite series presented in the problem is composed entirely of positive integers.  "0" is not a positive integer.  It makes no sense to include "the first zero terms" of the series in the summation formula.

Posted by Mindrod on 2007-05-17 00:33:26