$\"\"$

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The series is $\"\"$ .

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The corresponding function of the series is $\"\"$ .

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$\"\"$ .

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Consider $\"\"$ .

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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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$\"\"$

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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Integral test:

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Find $\"\"$ .

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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 convergent.

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Since the integral is convergent, the series $\"\"$ is convergent.

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$\"\"$

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The series $\"\"$ is convergent.