Use Mathematical Induction to Prove the Following$$1 \cdot 3 + 2 \cdot 4 + 3 \cdot 5 + \ldots + n ( n + 2 ) = \frac { n ( n + 1 ) ( 2 n + 7 ) } { 6 }$$

Question

Examlex · Accepted Answer

The Answer of Use Mathematical Induction to Prove the Following$$1 \cdot 3 + 2 \cdot 4 + 3 \cdot 5 + \ldots + n ( n + 2 ) = \frac { n ( n + 1 ) ( 2 n + 7 ) } { 6 }$$

Use Mathematical Induction to Prove the Following $1 \cdot 3 + 2 \cdot 4 + 3 \cdot 5 + \ldots + n ( n + 2 ) = \frac { n ( n + 1 ) ( 2 n + 7 ) } { 6 }$

Definitions:

Use Mathematical Induction to Prove the Following 1⋅3+2⋅4+3⋅5+…+n(n+2)=n(n+1)(2n+7)61 \cdot 3 + 2 \cdot 4 + 3 \cdot 5 + \ldots + n ( n + 2 ) = \frac { n ( n + 1 ) ( 2 n + 7 ) } { 6 }1⋅3+2⋅4+3⋅5+…+n(n+2)=6n(n+1)(2n+7)​

Definitions:

Use Mathematical Induction to Prove the Following $1 \cdot 3 + 2 \cdot 4 + 3 \cdot 5 + \ldots + n ( n + 2 ) = \frac { n ( n + 1 ) ( 2 n + 7 ) } { 6 }$