# Name this stupidly basic math function for meFebruary 28, 2009 6:56 PM   Subscribe

Basic Mathematical NameFilter: Name This Sequence

Is there a name for the mathematical function that means "The sum of N plus every number (n-1), from N to 0"?

For example function(5) = 5+4+3+2+1. Yes, the answer is 15, but what is the function called?

I'm looking for something like "the mathematical X of a number" or "the Y sequence" -- or perhaps "The Completely Basic Sequence Name that Everybody Who Paid Attention in Algebra Knows Off The Top Of Their Head"

I'm completely unable to Google this in a way that makes any sense, and yes, its driving me nuts. Please put me out of my misery.
posted by bhance to Education (10 answers total) 2 users marked this as a favorite

Best answer: I am not a mathematician (and also not YOUR mathematician), but how about Triangular number?
posted by The Tensor at 7:01 PM on February 28, 2009 [1 favorite]

I don't believe there is a name for this. There is an amusing story invoving Karl Gauss, though. You'd think it would be called a "Gauss Sum," but that goes into set theory, with which I am unfamiliar.
posted by adipocere at 7:01 PM on February 28, 2009

I always knew it as the sum of the first n integers. But I can't recall any fancy name for it though.
posted by dnesan at 7:02 PM on February 28, 2009

Bah, I must have missed that one. You'd think they'd name it after Gauss. What gives? Does he just have too much stuff named after him already and they don't want all the other mathematicians to be jealous?
posted by adipocere at 7:03 PM on February 28, 2009 [1 favorite]

You probably mean the triangular numbers.

The optimal search strategy for integer sequences is surely to calculate the first few values and search the On-Line Encyclopedia of Integer Sequences.
posted by grouse at 7:04 PM on February 28, 2009

Somebody asked Google a while back. Remember when you could do that?
posted by pullayup at 7:07 PM on February 28, 2009

Response by poster: Sweet jesus thank you Tensor & Grouse for finding that.

posted by bhance at 7:13 PM on February 28, 2009

It's also an arithmetic series from 1 to n with 1 added between terms. There are other arithmetic series, varying on the starting point and the difference between the successive terms in the sum; e.g. 5+8+11+14+17+20 is another arithmetic series.
posted by Anything at 7:50 PM on February 28, 2009

Anyone who has this kind of question in the future, the place to look first is The On-Line Encyclopedia of Integer Sequences!
posted by dfan at 8:06 PM on February 28, 2009

Arithmetic Series:
n = n(n+1)/2
This is the trick Gauss used as a schoolboy to solve the problem of summing the integers from 1 to 100 given as busy-work by his teacher. While his classmates toiled away doing the addition longhand, Gauss wrote a single number, the correct answer
1/2(100)(1+100)=50ยท101=5050

posted by weapons-grade pandemonium at 10:42 PM on February 28, 2009

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