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What is the term for a factorial type operation, but with summation instead of products?

Is there a similar function for the addition operator as there is the factorial function for the multiplication operator?

For factorials it is 5! = 5*4*3*2*1, is there a function that would do 5+4+3+2+1?



marked as duplicate by Gerry Myerson, t.b., Willie Wong Jun 25 '12 at 13:27

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  • $\begingroup$ yes, n(n+1)/2 :) $\endgroup$ – Aang Jun 25 '12 at 13:16

As far as I know we haven't given that expression a name since we may write it explicitly as $$ \sum_{i=1}^ni = {n+1 \choose 2} = \frac{n(n+1)}{2}. $$

  • $\begingroup$ we can do the same thing using a \Pi, why do we have the factorial function ..? Though it's not closed form yes. $\endgroup$ – Eiyrioü von Kauyf Aug 5 '13 at 16:33
  • $\begingroup$ @EiyrioüvonKauyf yes that is true. Pure speculation on my part, but writing $1\cdot 2\cdots n$ is not "nice enough" notation and $n!$ comes up "more frequently" that a shorter notation was needed. If one really needs a shorter notation for $\sum_1^n i$, I supposed one would just refer to it as $T_n$, the $n$th triangle number. $\endgroup$ – nullUser Aug 5 '13 at 17:10
  • $\begingroup$ mhmm I've seen that notation before somewhere :) $\endgroup$ – Eiyrioü von Kauyf Aug 5 '13 at 17:12

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