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Does $\sum_{n=1}^\infty \dfrac{5\ln{n}}{n^7}$ converge?
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Does $\sum_{n=1}^\infty \dfrac{n-1}{n^2\sqrt{n}}$ converge or diverge?
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Does $\sum_{n=1}^\infty \dfrac{5n^4 - 3n^3 + 12n^2 + 54n - 78}{27n^5 + 15n^2 + 54n - 78}$ converge or diverge?
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Does $\sum_{n=1}^\infty \dfrac{n}{\sqrt{n^5 + 3}}$ converge or diverge?
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Does $\sum_{n=1}^\infty \dfrac{8n^{10} - n^6 + 5\sqrt{n}}{n^{12} - n^7 + 2}$ converge or diverge?