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Use the Principle of Mathematical Induction to Show That the Statement

Question 138

Essay

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
- 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 }

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First we show that the statement is true...

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