Calculus

# Infinite sequences and series

- Defining convergent and divergent infinite series
- Working with geometric series
- The nth-term test for divergence
- Integral test for convergence
- Harmonic series and p-series
- Comparison tests for convergence
- Alternating series test for convergence
- Ratio test for convergence
- Determining absolute or conditional convergence
- Alternating series error bound
- Finding Taylor polynomial approximations of functions
- Lagrange error bound
- Radius and interval of convergence of power series
- Finding Taylor or Maclaurin series for a function
- Representing functions as power series

Register for a session to review this topic with a small group of learners.

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Calculus · series session

#### Infinite sequences and series

Infinite series: foundations, some tests, Taylor polynomials!

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LG

Luca G

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16/200

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Calculus · series session

#### Infinite sequences and series

Final Unit of AP Calculus BC

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SJ

Sahasra J

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19/30

Is

Calculus · series session

#### Infinite sequences and series

We will solve problems from unit 10 of the AP Calculus BC Course

BL

SJ

Sahasra J

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19/30

Is

Calculus · series session

#### Infinite sequences and series

10.1 - What is convergence versus divergence of an infinite series?

10.2 - When does a geometric series converge, and to what sum?

10.3 - What does the nth term test tell us?

10.4 - When do we use the integral test?

10.5 - When do we use the p-series test?

10.6 - When do we use the direct and limit comparison tests?

10.7 - When do we use the alternating series test?

10.8 - When do we use the ratio test?

10.9 - How do we determine absolute and conditional convergence of a series?

10.10 - What is the error bound for a partial sum of an alternating series?

BL

WB

William B

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10/50

Is

Calculus · series session

#### Infinite sequences and series

10.11 - What are Taylor polynomials?

10.12 - How can we determine the error bound for a taylor approximation of a function?

10.13 - How can we determine the interval of convergence for an infinite series with x, if we use the ratio test?

10.14 - How do we calculate the taylor series for a function?

10.15 - How do we integrate or differentiate functions represented as infinite series?

BL

WB

William B

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10/50

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