Pre-Calculus Final: Series

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Define a geometric series.

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A geometric series is a series of terms where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

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What is the formula for the sum of a finite geometric series?

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The sum S of the first n terms of a finite geometric series can be calculated using the formula: S = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio.

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Define an arithmetic series.

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An arithmetic series is a series of numbers in which the difference between consecutive terms is constant, known as the common difference.

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What is the formula for the sum of an arithmetic series?

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The sum S of the first n terms of an arithmetic series can be calculated using the formula: S = n/2 * (a + l), where a is the first term, l is the last term, and n is the number of terms.

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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 is the formula for the sum of an infinite geometric series?

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The sum S of an infinite geometric series exists if the absolute value of the common ratio r is less than 1, and is given by S = a / (1 - r), where a is the first term.