# Is there a way to quickly know the number of elements on a triangle type? [duplicate]

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 Guess who it is., Byron Schmuland, Hans Lundmark, t.b., RasmusOct 3 '11 at 13:33

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

## 1 Answer

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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