INFINITE GEOMETRIC SERIES

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What is an infinite geometric series?

Back

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.

Front

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).

Front

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

Back

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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Back

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