Understanding Infinite Geometric Series

The video tutorial explains how to determine if alternating infinite geometric series converge or diverge. It covers the conditions for convergence, where the absolute value of the common ratio r is less than one, and divergence, where it is greater than or equal to one. Two examples are provided: one with a converging series where r = -1/3, resulting in a sum of 3/4, and another with a diverging series where r = -9/7, which does not have a sum.

What condition must the absolute value of the common ratio 'r' satisfy for an infinite geometric series to converge?

• r must be less than 1

• r must be greater than 1

• r must be greater than or equal to 1

• r must be equal to 1

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CCSS.HSF.BF.A.2

In the first example, what is the common ratio 'r' of the series?

• -1/3

• 3

• 1/3

• -3

What is the sum of the series in the first example?

• 4/3

• 1/3

• 3/4

• 1/4

Why does the series in the first example converge?

• Because the common ratio is greater than 1

• Because the first term is 1

• Because the common ratio is less than 1

• Because the series is finite

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CCSS.HSF.BF.A.2

In the second example, what is the common ratio 'r' of the series?

• -9/7

• 9/7

• -7/9

• 7/9

Why does the series in the second example diverge?

• Because the series is finite

• Because the common ratio is greater than or equal to 1

• Because the common ratio is equal to 1

• Because the common ratio is less than 1

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CCSS.HSF.BF.A.2

What is the first term of the series in the second example?

• -9/7

• 1

• 0

• 9/7

What happens to the series when the absolute value of the common ratio is greater than or equal to 1?

• The series converges

• The series diverges

• The series becomes finite

• The series oscillates

What is the absolute value of the common ratio in the second example?

• 1

• 7/9

• 9/7

• 0

Can the sum of the series in the second example be calculated? Why or why not?

• Yes, because the series is finite

• No, because the series is infinite

• No, because the series diverges

• Yes, because the series converges