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

(Pardon if this seems a bit beginner, this is my first post in math – trying to improve my knowledge while tackling Project Euler problems)

I’m aware of Sigma notation, but is there a function/name for e.g.


similar to 4!=4321, which uses multiplication?

Edit: I found what I was looking for, but is there a name for this type of summation?


The name for

T_n= \sum_{k=1}^n k = 1+2+3+ \dotsb +(n-1)+n = \frac{n(n+1)}{2} = \frac{n^2+n}{2} = {n+1 \choose 2}

is the nth triangular number. This picture demonstrates the reasoning for the name:

T_1=1\qquad T_2=3\qquad T_3=6\qquad T_4=10\qquad T_5=15\qquad T_6=21

\hskip1.7in enter image description here

Source : Link , Question Author : barfoon , Answer Author : TW80000

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