$\"\"$

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The given geometric series $\"\"$ .

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The sum of a geometric series is $\"\"$ .

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Where $\"\"$ is first term and r is common ratio.

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Method 1

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Subtract denominator: $\"\"$ )

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$\"\"$ (Evaluate power: $\"\"$ )

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$\"\"$ (Subtract numerator: $\"\"$ )

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$\"\"$ (Divide: $\"\"$ ) $\"\"$

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Method 2

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Find the terms by replacing n with 1, 2, 3, 4, 5, 6, 7, 8 and 9.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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= 2,555

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$\"\"$

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The sum of the geometric series is 2,555.