Write the Statements S K and S K +1$$S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$$

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The Answer of Write the Statements S K and S K +1$$S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$$

Write the Statements S_k and S_k+1 $S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$

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Write the Statements Sk and Sk+1 Sn:1⋅2+2⋅3+3⋅4+…+n(n+1)=n(n+1)(n+2)3S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }Sn​:1⋅2+2⋅3+3⋅4+…+n(n+1)=3n(n+1)(n+2)​

Definitions:

Write the Statements S_k and S_k+1 $S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$