## Is there a concept equivalent to factorial that uses addition rather than multiplication? [closed]

I have a list of items, that all need to be linked.

To determine the count for 4 linked items (in terms of established links)

you start at 3

3 + 2 + 1 which yields 6

Every preceding integer value.

Another example To get the link count for 5 items you do

4+3+2+1 yields 10

Is there a term for this? It is similar to factorials in the sense that every preceding integer value is used, but different in that the operator is addition in stead of multiplication.

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It's called $\frac{n(n+1)}{2}$. You can either think a little bit to find a proof, or use induction. – Helge Jun 17 2010 at 11:32
They are sometimes called triangular numbers. In any case, this questions is not appropriate for MO. See the FAQ for some reasons. – Harald Hanche-Olsen Jun 17 2010 at 11:41

## closed as off topic by Steve Huntsman, Harald Hanche-Olsen, gowers, Gjergji Zaimi, Joel David HamkinsJun 17 2010 at 12:36

They are called triangular numbers.

http://en.wikipedia.org/wiki/Triangular_number

http://www.research.att.com/~njas/sequences/A000217

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It's best not to answer questions that are obviously inappropriate -- please just leave a comment directing people to the FAQ or an alternative site. – Scott Morrison Jun 17 2010 at 19:50

The comment by Helge is correct. They even have a name - the Triangular numbers.

Slightly more interesting is the same idea but for $\frac{1}{i}$ and addition gives you the harmonic numbers.

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