The presenter should have shown that 9 + 5n is less than something (not greater than) since we are dividing by it. Rather than \(9 + 5n ≥ 5n\), he should have shown \(9+5n ≤2·5n\). This follows from \(9<5^2 ≤ 5^n\) for \(n≥2\) and so \(9+5^n <5^n +5^n =2·5^n\). Note the final answer is the same in that the series diverges, but with \(1/4\) in front instead of \(1/2\).
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WIR 20B M152 V55