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Prove the following by the principle of mathematical induction: `\ 1. 2+2. 3+3. 4++n(n+1)=(n(n+1)(n+2))/3`

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To prove the statement \( P(n) : 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n(n + 1) = \frac{n(n + 1)(n + 2)}{3} \) by the principle of mathematical induction, we will follow these steps: ### Step 1: Base Case We need to check if the statement is true for \( n = 1 \). **Left-hand side (LHS)**: \[ P(1) = 2 ...
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