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?
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Is it a Sequence? – whytheq May 12 '19 at 21:24
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@AndreasRejbrand I am wondering what is the name of this thing? – samol May 12 '19 at 21:25
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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 $
DjaouadNM
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@TSR The second part isn't $(n + 1) / 2$, it's the Binomial coefficient, or the Combination, it is read as "$n + 1$ choose $2$" and computes the number of possible combinations of size $2$ from a set of size $n + 1$. – DjaouadNM Mar 16 '23 at 21:01