# Unit 12: Series

## About this unit

Series are sums of multiple terms. Infinite series are sums of an infinite number of terms. Don't all infinite series grow to infinity? It turns out the answer is no. Some infinite series converge to a finite value. Learn how this is possible and how we can tell whether a series converges and to what value. We will also learn about Taylor and Maclaurin series, which are series that act as functions and converge to common functions like sin(x) or eˣ. (This content belongs in AP Calc BC only, and not in AP Calc AB.)

### Learn

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- Sequences reviewGet 3 of 4 questions to level up!
- Sequence convergence/divergenceGet 3 of 4 questions to level up!

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- Partial sums introGet 3 of 4 questions to level up!
- Partial sums & seriesGet 3 of 4 questions to level up!

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- Infinite geometric seriesGet 3 of 4 questions to level up!

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- nth term testGet 3 of 4 questions to level up!
- Integral testGet 3 of 4 questions to level up!
- p-seriesGet 3 of 4 questions to level up!

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- Direct comparison testGet 3 of 4 questions to level up!
- Limit comparison testGet 3 of 4 questions to level up!

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- Ratio testGet 3 of 4 questions to level up!
- Alternating series testGet 3 of 4 questions to level up!

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- Interval of convergenceGet 3 of 4 questions to level up!
- Integrate & differentiate power seriesGet 3 of 4 questions to level up!

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- Taylor & Maclaurin polynomialsGet 3 of 4 questions to level up!
- Lagrange error boundGet 3 of 4 questions to level up!

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- Maclaurin series of sin(x), cos(x), and eˣGet 3 of 4 questions to level up!

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- Function as a geometric seriesGet 3 of 4 questions to level up!
- Integrals & derivatives of functions with known power seriesGet 3 of 4 questions to level up!