(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⟶10,

similar to 4!=4⋅3⋅2⋅1, which uses multiplication?

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

**Answer**

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

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