Series and Sequences

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What is a series?

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A series is the sum of the terms of a sequence.

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What is a sequence?

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A sequence is an ordered list of numbers that follow a particular pattern.

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What is the difference between finite and infinite series?

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A finite series has a limited number of terms, while an infinite series continues indefinitely.

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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 specific value as more terms are added.

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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 specific value.

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How do you find the sum of a finite arithmetic series?

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Use the formula S_n = n/2 * (a + l), where S_n is the sum, n is the number of terms, a is the first term, and l is the last term.

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What is an arithmetic sequence?

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An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

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What is the common difference in an arithmetic sequence?

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The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence.

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How do you find the next term in an arithmetic sequence?

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Add the common difference to the last known term.

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What is a geometric series?

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A geometric series is the sum of the terms of a geometric sequence, where each term is multiplied by a constant factor.