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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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  • $\begingroup$ Is it a Sequence? $\endgroup$
    – whytheq
    May 12, 2019 at 21:24
  • $\begingroup$ @AndreasRejbrand I am wondering what is the name of this thing? $\endgroup$
    – samol
    May 12, 2019 at 21:25

1 Answer 1

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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 $

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  • $\begingroup$ why did n(n+1)/2 become (n+1)/2 ? Shouldn't it be (n^2 + n)/2 ? $\endgroup$
    – TSR
    Mar 16, 2023 at 1:43
  • $\begingroup$ @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 $n + 1$. $\endgroup$
    – DjaouadNM
    Mar 16, 2023 at 21:01

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