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Prove by using the principle of mathematical induction that for all `n in N, 10^(n)+3.4^(n+2)+5` is divisible by 9

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To prove that \(10^n + 3 \cdot 4^{n+2} + 5\) is divisible by 9 for all \(n \in \mathbb{N}\), we will use the principle of mathematical induction. ### Step 1: Base Case We start with the base case \(n = 1\). \[ 10^1 + 3 \cdot 4^{1+2} + 5 = 10 + 3 \cdot 4^3 + 5 \] ...
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