Series Convergence and Divergence

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What is a series in mathematics?

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A series is the sum of the terms of a sequence. It can be finite or infinite.

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What does it mean for a series to converge?

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A series converges if the sum of its terms approaches a finite limit as the number of terms increases.

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What does it mean for a series to diverge?

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A series diverges if the sum of its terms does not approach a finite limit as the number of terms increases.

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What is the formula for the geometric series?

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What is the ratio test for convergence?

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What is the root test for convergence?

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What is the comparison test for convergence?

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What is the integral test for convergence?

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What is the alternating series test?

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The alternating series test states that if the terms of the series alternate in sign and decrease in absolute value to zero, the series converges.

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