Prove the following by using the principle of mathematical induction for all `n in N`:`(2n+7)<(n+3)^2`.

Explanation

To prove the statement \( 2n + 7 < (n + 3)^2 \) 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, which is \( n = 1 \).

\[ 2(1) + 7 = 2 + 7 = 9 \]
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