$\"\"$

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The series is $\"\"$ .

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$\"\"$

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$\"\"$

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Root test :

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Let $\"\"$ be a series.

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1. $\"\"$ converges absolutely if $\"\"$ .

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2. $\"\"$ diverges if $\"\"$ or $\"\"$ .

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3. The root test is inconclusive if $\"\"$ .

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Consider $\"\"$ .

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Find $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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

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$\"\"$

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$\"\"$ is convergent.