$\"\"$ \ \

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Integral test: \ \

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Suppose $\"\"$ is a continuous, positive, decreasing function on $\"\"$ and let $\"\"$ . \ \

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Then the series $\"\"$ is convergent if and only if the improper integral $\"\"$ is convergent. \ \

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(i) If $\"\"$ is convergent, then $\"\"$ is convergent. \ \

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(ii) If $\"\"$ is divergent, then $\"\"$ is divergent. \ \

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$\"\"$

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The series is $\"\"$ .

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Using integral test: \ \

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Consider the integral $\"\"$ .

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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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$\"\"$ .

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The integral is diverges. \ \

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Therefore, the series $\"\"$ is diverges. \ \

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$\"\"$

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The series $\"\"$ is diverges. \ \