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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 with first term a and common ratio r (|r| < 1) is given by: S = a / (1 - r).

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Given the first term 318 and common ratio 1/2, what is the sum of the infinite geometric series?

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The sum is 636.

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Evaluate the infinite geometric series: 3 - 2 + 4/3 - 8/9 + ...

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The sum is 9/5.

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The sum is 5.

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What does it mean if a geometric series diverges?

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A geometric series diverges if the absolute value of the common ratio is greater than or equal to 1, meaning the sum does not approach a finite limit.

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Find the sum of the infinite geometric series: 200 - 100 + 50 - 25 + ...

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The sum is 400/3.

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What is the common ratio in the series 3 - 2 + 4/3 - 8/9 + ...?

Back

The common ratio is -2/3.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of a geometric series is 5 and the common ratio is 1/3, what is the sum?

Back

The sum is 5 / (1 - 1/3) = 7.5.

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Back

Tags

CCSS.HSF.BF.A.2