Use Mathematical Induction to Prove That for All Integers $n \geq 3$

Essay

Use mathematical induction to prove that for all integers $n \geq 3$ ,
$$2 \cdot 3 + 3 \cdot 4 + \cdots + ( n - 1 ) \cdot n = \frac { ( n - 2 ) \left( n ^ { 2 } + 2 n + 3 \right) } { 3 } .$$