$\"\"$

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Integral test: \ \

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

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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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The function $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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For $\"\"$ the value of $\"\"$ . \ \

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If the function $\"\"$ is decreasing in the interval $\"\"$ , then $\"\"$ in the interval $\"\"$ .

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Threfore, the integral test cannot be applicable to find the series is converges.

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$\"\"$

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The function $\"\"$ is not monotonically decreasing.