Prove the following by using the principle of mathematical induction for all `n in N`:`(1+3/1)(1+5/4)(1+7/9)...(1+((2n+1))/(n^2))=(n+1)^2`

Explanation

To prove the statement \((1 + \frac{3}{1})(1 + \frac{5}{4})(1 + \frac{7}{9}) \cdots (1 + \frac{2n + 1}{n^2}) = (n + 1)^2\) 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, \(n = 1\).

**LHS for \(n = 1\):**
\[
LHS = 1 + \frac{3}{1} = 1 + 3 = 4
...