$\"\"$

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Theorem 9.9 :

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$\"\"$ Term test for divergence: $\"\"$ then $\"\"$ diverges.

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$\"\"$

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The series is $\"\"$ .

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If $\"\"$ is convergent, then $\"\"$ .

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Consider $\"\"$ .

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Since the limit is in indeterminant form $\"\"$ , apply L $\"\"$ Hopital $\"\"$ s Rule.

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L $\"\"$ Hopital $\"\"$ s Rule:

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For $\"\"$ If $\"\"$ or $\"\"$ then $\"\"$ .

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$\"\"$

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Derivative formula: $\"\"$ .

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$\"\"$

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$\"\"$ .

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Therefore, the sequence is divergent.

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$\"\"$

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$\"\"$ is divergent.