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

Explanation

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

### Step 1: Base Case
We start by checking the base case for \(n = 1\).

**Left-Hand Side (LHS):**
\[
1 \cdot 2 \cdot 3 = 6
...