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Prove the following by using the princip...

Prove the following by using the principle of mathematical induction for all `n in N`:`1 + 2 + 3 + ... + n <1/8(2n+1)^2`.

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To prove the statement \(1 + 2 + 3 + \ldots + n < \frac{1}{8}(2n + 1)^2\) for all \(n \in \mathbb{N}\) using the principle of mathematical induction, we will follow these steps: ### Step 1: Base Case We first check the base case \(n = 1\). **LHS:** \[ 1 ...
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