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

Question 1

(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.

$4 + 3 + 2 + 1 \longrightarrow 10 ,$

similar to $4! = 4 \cdot 3 \cdot 2 \cdot 1 ,$ which uses multiplication?

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

Question 2

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 $n$ th 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

Answer