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 \((1+\frac{3}{1})(1+\frac{5}{4})(1+\frac{7}{9})\ldots(1+\frac{(2n+1)}{n^2})=(n+1)^2\) 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 \(n = 1\).

**Left Hand Side (LHS):**
\[
(1 + \frac{3}{1}) = 1 + 3 = 4
...