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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.

Thanks in advance.

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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 Hamkins Jun 17 2010 at 12:36

2 Answers

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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
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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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