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

Question

Examlex · Accepted Answer

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

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

Definitions:

Use Mathematical Induction to Prove the Following 1⋅2+2⋅3+3⋅4+…+n(n+1)=n(n+1)(n+2)31 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }1⋅2+2⋅3+3⋅4+…+n(n+1)=3n(n+1)(n+2)​

Definitions:

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