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

Explanation

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
...