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

I don't technically know the mathematical term, but imagine:

         X
        X X
       X X X
      X X X X
     X X X X X
    X X X X X X
   X X X X X X X
  X X X X X X X X
 X X X X X X X X X
X X X X X X X X X X

taking the last row that holds 10 elements, the total will be:

10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 

witch totals 55

just like there is the factor sign 10! that tells us the same but multiplying the numbers, is there a technical term / function, to by other means calculate the total 55?

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marked as duplicate by J. M., Byron Schmuland, Hans Lundmark, t.b., Rasmus Oct 3 '11 at 13:33

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1 Answer

up vote 3 down vote accepted

Yes there is, the triangular numbers, and they can be calculated very easily: $$T_n=\frac{n(n+1)}{2}.$$ Your particular example is $T_{10}=(10\cdot 11)/2=55$.

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