Prove the following by using the principle of mathematical induction for all `n in N`:`1. 2 + 2. 3 + 3. 4 + ...+ n(n + 1)=[(n(n+1)(n+2))/3]`

Explanation

To prove the statement \( 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n(n + 1) = \frac{n(n + 1)(n + 2)}{3} \) for all \( n \in \mathbb{N} \) using the principle of mathematical induction, we will follow these steps:

### Step 1: Base Case
We need to check if the statement holds true for \( n = 1 \).

**Left Hand Side (LHS):**
\[
LHS = 1 \cdot 2 = 2
...