<s>[INST] What is $(N)+ (N-1) + (N -2) + \cdots + 1$ called? This is purely for figuring the name of a mathematical concept.
For example, $N \times (N-1) \times \cdots \times  1$ is called factorial.
Question: What is $N + (N-1) + (N -2) + \cdots + 1$ called?
 [/INST] The sum of numbers from $1$ to $n$ is called a "Triangular number".
From Wikipedia:

The triangle numbers are given by the following explicit formulas:
$$T_n = \sum_{k=1}^n{k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}{2}} = \binom{n + 1}{2},$$

So, the first triangular numbers are:
$
    T_1 = 1\\
    T_2 = 1 + 2 = 3\\
    T_3 = 1 + 2 + 3 = 6\\
    T_4 = 1 + 2 + 3 + 4 = 10\\
    ...etc
$
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