TITLE: Is there a way to denote the calculation $1+2+3+\dots+n$?
QUESTION [18 upvotes]: Since $n!$ represents $$1\cdot2\cdot3\cdots n,$$ I am wondering if there is a way to represent  $$1+2+3+\dots+n?$$
What are some usual notations for the computation of some common sequences? Any other examples?

REPLY [3 votes]: Another way to write it would be ${n+1 \choose 2}$:
${n \choose 0}=1$ for all $n$, and ${n \choose k+1} = \sum_{k=0}^{n-1}{n \choose k}$ (with ${0 \choose k} = 0$ for $k>0$). Therefore ${n\choose 1}=n$ and thus ${n+1 \choose 2}=\sum_{k=0}^n k$. Note that this actually is $0+1+\dots+n$, but obviously the additional term $0$ doesn't change the sum.