Question

What is the equation for a sequence that goes 0,1,3,6,10,15 (+1, +2, +3, +4 .....)

Answer 1

\[S_1=0\]\[S_2=0+1=1\]\[S_3=0+1+2=3\]\[\vdots\]\[S_n=0+1+2+\cdots+(n-1)=\frac{n(n-1)}{2}\]