AP Calculus BC · Unit 10
Infinite Sequences and Series
In short
Unit 10: Infinite Sequences and Series in AP Calculus BC covers 15 topics: Defining Convergent and Divergent Infinite Series, Working with Geometric Series, The nth Term Test for Divergence, Integral Test for Convergence and 11 more. Open each one for what you need to know, a self-check list and how it is tested on the exam.
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What is in Unit 10: Infinite Sequences and Series?
Unit 10: Infinite Sequences and Series
10.1 Defining Convergent and Divergent Infinite Series
10.2 Working with Geometric Series
- 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).
10.3 The nth Term Test for Divergence
- I can use the nth term test to determine if a series diverges.
10.4 Integral Test for Convergence
10.5 Harmonic Series and p-Series
- I can identify the harmonic series, the alternating harmonic series, and p-series, and use them to determine whether a series converges or diverges.
10.6 Comparison Tests for Convergence
10.7 Alternating Series Test for Convergence
10.8 Ratio Test for Convergence
10.9 Determining Absolute or Conditional Convergence
- I know that rearranging or regrouping the terms of an absolutely convergent series does not change its value.
10.10 Alternating Series Error Bound
10.11 Finding Taylor Polynomial Approximations of Functions
- I can explain that as the degree of a Taylor polynomial increases, it approaches the original function over some interval.
- I can use a Taylor polynomial centered at x = a to approximate function values near x = a.
10.12 Lagrange Error Bound
10.13 Radius and Interval of Convergence of Power Series
- I can recognize the standard form of a power series.
- I know that a power series converges either at a single point or on an interval of convergence.
- I can test both endpoints of an open interval to determine the full interval of convergence for a power series.
- I know that term-by-term differentiation or integration of a power series does not change its radius of convergence.
10.14 Finding Taylor or Maclaurin Series for a Function
10.15 Representing Functions as Power Series
- I can derive a power series for a given function by applying operations like term-by-term differentiation, integration, algebraic processes, or substitutions to a known series.
Infinite Sequences and Series: common questions
What is in Unit 10: Infinite Sequences and Series?
It covers 15 topics: 10.1 Defining Convergent and Divergent Infinite Series; 10.2 Working with Geometric Series; 10.3 The nth Term Test for Divergence; 10.4 Integral Test for Convergence; 10.5 Harmonic Series and p-Series; 10.6 Comparison Tests for Convergence; 10.7 Alternating Series Test for Convergence; 10.8 Ratio Test for Convergence; 10.9 Determining Absolute or Conditional Convergence; 10.10 Alternating Series Error Bound; 10.11 Finding Taylor Polynomial Approximations of Functions; 10.12 Lagrange Error Bound; 10.13 Radius and Interval of Convergence of Power Series; 10.14 Finding Taylor or Maclaurin Series for a Function; 10.15 Representing Functions as Power Series.
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