$\"\"$

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The series is $\"\"$ and $\"\"$ .

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The first term is less than $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ or $\"\"$

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$\"\"$ or $\"\"$ .

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The value of the $\"\"$ is always positive.

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$\"\"$

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The first term is less than $\"\"$ for $\"\"$ .

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$\"\"$

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The series is $\"\"$ .

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The first term is less than $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The first term is less than $\"\"$ for $\"\"$ .

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The series $\"\"$ is less than $\"\"$ for $\"\"$ and the series $\"\"$ is less than $\"\"$ for $\"\"$ .

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Therefore, the series $\"\"$ is converges at a higher rate.

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$\"\"$

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The series $\"\"$ is converges at a higher rate.