Test the following series for convergence or divergence. Justify the decision.
Let
Then we apply the limit comparison test,
Hence, the series and
either both converge or both diverge. But we know
diverges (by the integral test, Example #1 on page 398 of Apostol). Hence,
diverges.
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Awesome solution. Slight error, should be $4n^2-16n+3$ not $4n^2-17n+3$. Doesn’t affect the logic, however.