Suppose we want to prove the statement $S(n):$ $"$If $n\geq 2,$ the sum of the integers $2$ through $n$ is $\frac{(n+2)(n-1)}{2}"$
by induction on $n.$ To prove the inductive step$,$ we can make use of the fact that
$2+3+4+......+(n+1)=(2+3+4+.....+n)+(n+1)$
Find$,$ in the list below an equality that we may prove to conclude the inductive part.
