Sum of First n Natural NumbersDate: 12/03/2005 at 01:35:34 From: Kevin Subject: the additive analog of a factorial The product of a series of consecutive integers is called a factorial. This seems to be a standard term and even has a standard symbol (!). It's defined that n! = 1*2*3*...*n. Is there a similar term for the sum of consecutive integers (1+2+3+...+n)? If so, what is it, and does it have a standard symbol? Date: 12/03/2005 at 23:22:34 From: Doctor Peterson Subject: Re: the additive analog of a factorial Hi, Kevin. A lot of people ask us this. Some ask if there is a "summorial", or something like that! The sum of the first n natural numbers is called the nth triangular number. This is because it can be seen as the number of dots in a triangle like this, the 5th triangular number: o o o o o o = 1+2+3+4+5 = 15 o o o o o o o o o There is no real symbol for it, in the sense of the factorial symbol, probably because it is easily calculated, as n(n+1)/2 (unlike the factorial, which is very hard to get without doing the multiplications). But the nth triangular number is often written as something like T n with the n as a subscript. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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