AP Calculus BC · Unit 10: Infinite Sequences and Series
10.2 Working with Geometric Series
In short
This topic introduces geometric series, defining them as series with a constant ratio between successive terms. You are expected to determine the convergence or divergence of a geometric series based on the value of the common ratio, specifically that it converges if the absolute value of the ratio is less than 1.
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What else do you need to know about Working with Geometric Series?
Furthermore, you must be able to calculate the sum of a convergent geometric series using the formula a/(1-r). This content is exclusively assessed on the AP Calculus BC exam.
Can you do these?
- I can identify a geometric series by verifying that there is a constant ratio between successive terms.
- I can determine whether a geometric series converges by checking if |r| < 1, and I can calculate its sum using the formula a/(1-r).
How is Working with Geometric Series tested on the exam?
You will be assessed on your ability to recognize geometric series and apply the geometric series test to determine convergence or divergence. You must also be able to evaluate the infinite sum of a convergent geometric series. The suggested skill for this topic is 3.D (Apply an appropriate mathematical definition, theorem, or test), meaning you should be prepared to formally justify the convergence or divergence of a geometric series by referencing its common ratio.
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Working with Geometric Series: common questions
What do you need to know about Working with Geometric Series for AP Calculus BC?
This topic introduces geometric series, defining them as series with a constant ratio between successive terms. You are expected to determine the convergence or divergence of a geometric series based on the value of the common ratio, specifically that it converges if the absolute value of the ratio is less than 1.
How is Working with Geometric Series tested on the AP Calculus BC exam?
You will be assessed on your ability to recognize geometric series and apply the geometric series test to determine convergence or divergence. You must also be able to evaluate the infinite sum of a convergent geometric series.
How do I know I have mastered Working with Geometric Series?
Check you can do each of these: identify a geometric series by verifying that there is a constant ratio between successive terms; determine whether a geometric series converges by checking if |r| < 1, and I can calculate its sum using the formula a/(1-r).
Where does Working with Geometric Series fit in AP Calculus BC?
Working with Geometric Series is topic 10.2 in Unit 10: Infinite Sequences and Series of AP Calculus BC.
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