Use the Deﬁnition of Big-O to Prove That$$1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \cdots + ( n - 1 ) \cdot n \text { is } O \left( n ^ { 3 } \right)$$

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Use the Deﬁnition of Big-O to Prove That $1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \cdots + ( n - 1 ) \cdot n \text { is } O \left( n ^ { 3 } \right)$

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Use the Deﬁnition of Big-O to Prove That 1⋅2+2⋅3+3⋅4+⋯+(n−1)⋅n is O(n3)1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \cdots + ( n - 1 ) \cdot n \text { is } O \left( n ^ { 3 } \right)1⋅2+2⋅3+3⋅4+⋯+(n−1)⋅n is O(n3)

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Use the Deﬁnition of Big-O to Prove That $1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \cdots + ( n - 1 ) \cdot n \text { is } O \left( n ^ { 3 } \right)$

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