Created on: September 9, 2008

Website Address: https://library.curriki.org/oer/MIT-OpenCourseWare--AP-Calculus--Series-of-Constants

TABLE OF CONTENTS

- MIT - Chemistry Laboratory Techniques
- MIT OpenCoruseWare - AP Physics - Kinematics
- MIT OpenCourseWare - AP Biology - Cells
- MIT OpenCourseWare - AP Biology - Heredity
- MIT OpenCourseWare - AP Biology - Ecology
- MIT OpenCourseWare - AP Physics - Electrostatics
- MIT OpenCourseWare - AP Physics - Electromagnetism
- MIT OpenCourseWare - AP Physics - Waves
- MIT OpenCourseWare - AP Biology - Chemistry of Life
- MIT OpenCourseWare - AP Physics - Kinetic Theory/Thermodynamics
- MIT OpenCourseWare - AP Physics - Geometric Optics
- MIT OpenCourseWare - AP Calculus - Analysis of Graphs
- MIT OpenCourseWare - AP Biology - Cellular Energetics
- MIT OpenCourseWare - AP Biology - Molecular Genetics
- MIT OpenCourseWare - AP Biology - Evolutionary Biology
- MIT OpenCourseWare - AP Biology - Diversity of Organisms
- MIT OpenCourseWare - AP Calculus - Limits of Functions
- MIT OpenCourseWare - AP Calculus - Second Derivatives
- MIT OpenCourseWare - AP Calculus - Applications of Derivatives
- MIT OpenCourseWare - AP Calculus - Computation of Derivatives
- MIT OpenCourseWare - AP Calculus - Applications of Integrals
- MIT OpenCourseWare - AP Calculus - Antidifferentiation Techniques
- MIT OpenCourseWare - AP Calculus - Applications of Antidifferentiation
- MIT OpenCourseWare - AP Calculus - Concept of Series
- MIT OpenCourseWare - AP Calculus - Series of Constants
- MIT OpenCourseWare - AP Calculus - Computation of Derivatives
- MIT OpenCourseWare - AP Physics - Work, Energy, Power
- MIT OpenCourseWare - AP Physics - Circular Motion & Rotation
- MIT OpenCourseWare - AP Physics - Oscillations & Gravitation
- MIT OpenCourseWare - AP Physics - Fluid Mechanics
- MIT OpenCourseWare - AP Physics - Temperature & Heat
- MIT OpenCourseWare - AP Physics - Conductors, Capacitors, Dielectrics
- MIT OpenCourseWare - AP Physics - Electric Circuits
- MIT OpenCourseWare - AP Physics - Magnetic Fields
- MIT OpenCourseWare - AP Physics - Physical Optics
- MIT OpenCourseWare - AP Physics - Atomic Physics & Quantum Effects
- MIT OpenCourse Ware - AP Calculus - Asymptotic & Unbounded Behavior
- MIT OpenCourseWare - AP Calculus - Continuity: Property of Functions
- MIT OpenCourseWare - AP Calculus - Parametric, Polar & Vector Functions
- MIT OpenCourseWare - AP Calculus - Parametric, Polar & Vector Functions
- MIT OpenCourseWare - AP Calculus - Concept of the Derivative
- MIT OpenCourseWare - AP Calculus - Derivative at a Point
- MIT OpenCourseWare - AP Calculus - Derivative as a Function
- MIT OpenCourseWare - AP Calculus - Fundamental Theorem of Calculus
- MIT OpenCourseWare - AP Physics - Newton's Laws of Motion
- MIT OpenCourseWare - AP Biology - Structure & Function of Plants & Animals
- MIT OpenCourseWare - AP Calculus - Interpretations & Properties of Definite Integrals
- MIT OpenCourseWare - AP Calculus - Numerical Approximations to Definite Integrals
- MIT OpenCourseWare - AP Physics - Systems of Particles, Linear Momentum

- MIT OpenCourseWare - AP Calculus - Continuity: Property of Functions - Continuity
- MIT OpenCourseWare - AP Calculus - Continuity: Property of Functions - Continuity in Terms of Limits

- MIT OpenCourseWare - AP Calculus - Series of Constants - Motivating Examples
- MIT OpenCourseWare - AP Calculus - Series of Constants - Geometric Series with Applications
- MIT OpenCourseWare - AP Calculus - Series of Constants - The Harmonic Series
- MIT OpenCourseWare - AP Calculus - Series of Constants - Alternating Series, Error Bound
- MIT OpenCourseWare - AP Calculus - Series of Constants - Series as Riemann Sums & the Integral Test
- MIT OpenCourseWare - AP Calculus - Series of Constants - Ratio Test, Convergence/Divergence
- MIT OpenCourseWare - AP Calculus - Series of Constants - Comparison Test

We have selected relevant material from MIT's introductory courses to support students as they study and educators as they teach the AP® Calculus curriculum. These do not comprise a full course of study but offer material to supplement the understanding of the AP Calculus curriculum.

Series of Constants covers the topics of motivating examples; geometric series with applications; harmonic series; alternating series (error bound); series as Riemann sums and the integral test; ratio test (convergence/divergence); and the comparison test using a mixture of lecture notes, textbook chapters, and exam questions.

Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA

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<The exam questions contained in this section of the AP Calculus materials cover motivating examples. Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

The exam questions contained in this section of the AP Calculus materials cover geometric series with applications. Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

The lecture notes contained in this section of the AP Calculus materials cover the harmonic series. Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

The lecture notes and textbook chapters contained in this section of the AP Calculus materials cover alternating series. Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

The lecture notes and textbook chapters contained in this section of the AP Calculus materials cover series as Riemann sums and the integral test. Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

The lecture notes, textbook chapters, and exam questions contained in this section of the AP Calculus materials cover the ratio test, convergence, and divergence. Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode

The lecture notes and exam questions contained in this section of the AP Calculus materials cover alternating series. Prof. David Jerison, 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Jason Starr, 18.01 Single Variable Calculus, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA Prof. Daniel J. Kleitman, 18.013A Calculus with Applications, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed October 28, 2008). License: Creative Commons BY-NC-SA http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm#cc http://creativecommons.org/licenses/by-nc-sa/3.0/us/legalcode