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Use Mathematical Induction to Prove the Statement Is True for All

Question 41

Essay

Use mathematical induction to prove the statement is true for all positive integers 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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