$\"\"$

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The series is $\"\"$ .

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Rewrite the series as $\"\"$ .

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The series is in the form of geometric series.

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Here the first term $\"\"$ and common ratio is $\"\"$ .

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If the series is cinverges, then $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Since sine function always lies between $\"\"$ for all values of $\"\"$ .

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Therefore, the interval of convergence is $\"\"$ .

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$\"\"$

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The sum of the series in geometric series is $\"\"$ .

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$\"\"$

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$\"\"$ .

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The sum of the series is $\"\"$ .

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$\"\"$

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Interval of convergence is $\"\"$ .

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The sum of the series is $\"\"$ .