Consider the following series. ∑n=2^∞(1)/(n^5/6

Consider the following series.\\ $\sum_{n=2}^{\infty} \frac{1}{n^{5/6} - 1}$ \\ Use the Direct Comparison Test to complete the inequality.\\ $\frac{1}{n^{5/6} - 1}$ --?-- \\ Determine the convergence or divergence of the series.\\ $\circ$ converges\\ $\circ$ diverges

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The provided text contains several errors, including typographical, grammatical, and mathematical errors. Here is the corrected version: Consider the following series: $$sum_{n=2}^{infty} frac{1}{n^{frac{5}{6}}-1}$$ Use the Direct Comparison Test to complete the inequality: $$frac{1}{n^{frac{5}{6}}-1} leq frac{1}{n^{frac{5}{6}}-n^{frac{1}{6}}}$$ Determine the convergence or divergence of the series: ◻ converges ◻ diverges Consider the following series: $$sum_{n=1}^{infty} frac{1}{n}$$ Use the Direct Comparison Test to complete the inequality: $$frac{1}{n} geq frac{1}{n+1}$$ Determine the convergence or divergence of the series: ◻ converges ◻ diverges Note: The second series provided is incomplete and does not specify the summand. I have assumed it to be the harmonic series for the purpose of correction. If the series is different, please provide the correct summand.

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Consider the following series.\\ $\sum_{n=2}^{\infty} \frac{1}{n^{5/6} - 1}$ \\ Use the Direct Comparison Test to complete the inequality.\\ $\frac{1}{n^{5/6} - 1}$ --?-- \\ Determine the convergence or divergence of the series.\\ $\circ$ converges\\ $\circ$ diverges

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