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

Question

Examlex · Accepted Answer

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

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

Definitions:

Use Mathematical Induction to Prove That the Statement Is True 3⋅5+4⋅6+5⋅7+…+(n+3)(n+5)=n(2n2+27n+115)63 \cdot 5 + 4 \cdot 6 + 5 \cdot 7 + \ldots + ( n + 3 ) ( n + 5 ) = \frac { n \left( 2 n ^ { 2 } + 27 n + 115 \right) } { 6 }3⋅5+4⋅6+5⋅7+…+(n+3)(n+5)=6n(2n2+27n+115)​

Definitions:

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