Infinite Geometric Series

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What is an infinite geometric series?

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An infinite geometric series is the sum of the terms of a geometric sequence that continues indefinitely. It converges if the absolute value of the common ratio is less than 1.

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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 can be calculated using the formula: S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio.

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What is the common ratio in a geometric series?

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The common ratio 'r' in a geometric series is the factor by which each term is multiplied to get the next term.

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How do you determine if an infinite geometric series converges?

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An infinite geometric series converges if the absolute value of the common ratio |r| is less than 1.

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What happens to the sum of an infinite geometric series if the common ratio is greater than or equal to 1?

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If the common ratio is greater than or equal to 1, the series diverges, meaning it does not have a finite sum.

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