Prove the following by the principle of mathematical induction: `\ 1^2+3^2+5^2++(2n-1)^2=1/3n(4n^2-1)`

Explanation

To prove the statement \(1^2 + 3^2 + 5^2 + \ldots + (2n - 1)^2 = \frac{1}{3}n(4n^2 - 1)\) using the principle of mathematical induction, we will follow these steps:

### Step 1: Base Case
We first check the base case \(n = 1\).

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