Use Mathematical Induction to Prove That the Statement Is True $$3 \cdot 5 + 4 \cdot 6 + 5 \cdot 7 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$$

Essay

Use mathematical induction to prove that the statement is true for every positive integer n.
- $$3 \cdot 5 + 4 \cdot 6 + 5 \cdot 7 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$$