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

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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 ...
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