A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these
statements is true.
-$$S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$$

Question

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The Answer of A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these
statements is true.
-$$S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$$

A Statement Sn About the Positive Integers Is Given 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)​

A Statement Sn About the Positive Integers Is Given $S _ { n } : 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$