>>11334201This is the set of triangular numbers. The first term in this sequence (call it is 1, the second is 1 + 1 = 2, the third is 1 + 1 + 2 = 4, ..., the term is . So we can express this set as
In general though, learning how to obtain the close form, non-recursive formula for a sequence is something you learn after practice and experience with various combinatorics, analysis, and some algorithm analysis, and you can learn to tackle the job directly with generating functions. This book is one of the best on the topic and is free online:
https://www.math.upenn.edu/~wilf/DownldGF.htmlAlso OEIS database is your friend. You can plug this sequence into the search bar and it’ll fetch it for you. These techniques are discussed in the “reading and doing mathematics” section of these slides:
http://www.cs.cmu.edu/~15751/2016-lecture1.pdf 
