(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