Use Mathematical Induction to Prove That the Statement Is True$$4 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$$

Question

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The Answer of Use Mathematical Induction to Prove That the Statement Is True$$4 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$$

Use Mathematical Induction to Prove That the Statement Is True $4 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$

Definitions:

Use Mathematical Induction to Prove That the Statement Is True 4⋅6+5⋅7+6⋅8+…+(n+3)(n+5)=n(2n2+27n+115)64 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }4⋅6+5⋅7+6⋅8+…+(n+3)(n+5)=6n(2n2+27n+115)​

Definitions:

Use Mathematical Induction to Prove That the Statement Is True $4 \cdot 6 + 5 \cdot 7 + 6 \cdot 8 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }$