Use the limit comparison test to prove convergence or divergence of the infinite series. please post the solution step by step with brief explanation, thank you!

$43. $ \sum_{n=3}^{\infty} \frac{3 n+5}{n(n-1)(n<2)} $$

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Use the limit comparison test to prove convergence or divergence of the infinite series. please post the solution step by step with brief explanation, thank you!

$43. $ \sum_{n=3}^{\infty} \frac{3 n+5}{n(n-1)(n<2)} $$

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