Let the increasing sequence of integers D: d₁, d₂, d₃, ...d_n-1, d_n... represent the sequence of consecutive differences of another sequence T: t₁, t₂, t₃, ...t_n-1, t_n.

Given t₁=0 , and t_k-t_k-1=d_k-1=k, provide definition and formula for the sequence T.

Steve H. identified the name of the sequence as "The Triangular Numbers". I would hate that fact to be lost. While our answers differed simply due to indices, he actually answered the challenge, which was to provide the name. I always learn something new here. I had to go to wikipedia to find the name origin. Interesting. So, I wondered if there are Tetrahedral Numbers, and indeed there are. They even count the total gifts in each verse of "The Twelve Days of Christmas" Thanks! 

Edited on September 17, 2018, 3:28 pm

Posted by Steven Lord on 2018-09-17 10:37:54