When you multiply all numbers from 1 to N, you call it N factorial (N!).
What is the word for when you add all numbers from 1 to N? Is there a word for it?
A triangular number.
If a mathematician wanted to express this concept in a lecture or the presentation of a paper, they would say “the summation from 1 to N”.
Thanks for the cite, but that’s not what I’m after. I’m looking for a shorter and simpler way to say “nine times the sum of all of the integers from 1 to N”, and “nine times the ninth triangular number” doesn’t make it simpler.
There’s a word for products - the product of all the integers from 1 to N is N! - but I can’t find one for sums.
Oops - that should have been “Nth triangular number” not “9th triangular number”.
“Nth triangular number” is much more concise than “the sum from 1 to N”, and it’s standard.
Yes, it’s more concise, but I’m writing an article for non-mathematicians, and that would introduce a whole new concept I’d have to explain. Maybe my memory’s just faulty, but I could have sworn there was a word for this.
I remember in the APL programming language, they used the Greek letter iota for this. In math classes, I was always taught to write it using the summation symbol with “i=1 to N”, followed by the letter i. Once again, too much to throw into the article.
I was hoping to be able to write something like, “The possible number of errors in this situation is ‘9 times iota N’, where ‘iota’ means adding together all of the numbers from 1 to N” (using the appropriate term instead of “iota”). Then, the other two times it comes up, I’ve got a word for it.
There’s not really a standard function on N for this. You could say early on in the article “Define a function T(n) as the sum of the first n positive integers” and then later refer to 9T(n).
Nope, no standard term that I can think of for the summation from 1 to n that is analogous to n! for the product from 1 to n. Probably because there’s not much use for that sum, unlike n! which is used a ton in combinatorics, binomial expansions, etc.
Better, I would think, to say “The sum of the first n positive integers is known as the nth ‘triangular number’” and then refer to triangular numbers later on. The words “define a function T(n)” alone will probably cause a non-mathematician’s eyes to glaze over.
Just to add my 2 cents:
The formula for determining that sum is:
n*(n+1)/2
For example the tenth triangular number is:
10 * 11 / 2 = 110 / 2 = 55
Well, thanks for the help, but I’m writing this for non-math types, and I think their eyes would glaze over halfway through that sentence. I think I’ll just gloss over the point in the main article and add a footnote explaining how it works.
Thanks for the comments, folks.
Since you’re writing it for non-math types, and you don’t know what the term is, that says to me that if you did find the “correct” term, your audience wouldn’t know what it meant.
Maybe I missed it, but what’s wrong with just saying “sum the numbers from 1 to N”?