Master AP Calculus BC Unit 10: Infinite Series

Learn all convergence tests, series behavior, and polynomial approximations

with clear explanations, step-by-step examples, and exam-level practice.

🎯 Complete Unit 10 Bundle - Best Value: Full theory and practice to master the entire unit.
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📄 Theory Notes Bundle (Clear, structured notes on all key concepts step by step):
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▶ Free Videos for all to understand key concepts
🔒 Full video access (all examples & exercises): Available with subscription

10.1 Defining Convergent and Divergent Infinite Series
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▶ Video 1: Key Definitions (infinite series, partial sum, convergence, divergence)
▶ Video 2: Connection between terms and partial sums

10.2 Geometric Series
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▶ Video 1: What is a geometric Series Free
▶ Video 2: Convergence criteria of a Geometric Series Free
▶ Video 3: The Sum Formula of a Geometric Series Free
▶ Video 4: Identifying the first term and the common ratio of a g.s. Free
▶ Video 5: Alternating Series (negative ratio) Free
🔒 Video 6: Working with parameters and variables Full access with subscription
🔒 Video 7: Geometric series with exponential and trigonometric forms
▶ Video 8: Finding Series from given information

10.4 Integral Test for Series Covergence
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▶ Video 1: Integral Test statement and methodology for exercises Free
▶ Video 2: 1 worked example on applying Integral Test for series convergence Free
🔒 Video 3: 4 more worked examples on Integral Test : Full access with subscription
▶ Video 4: Proving p-series convergence and divergence Free
▶ Video 5: Common mistakes to avoid Free

10.5 Harmonic series and P-series
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▶ Video 1: Introducing P-series  Free
▶ Video 2: Harmonic series as a special case of a P-series Free

10.6 Comparison Tests for Covergence
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▶ Video 1: Direct Comparison Test (DCT): statement and 1 worked example
🔒 Video 2: Exercise: Direct Comparison Test with Logarithmic terms
🔒 Video 3: Exercise: Direct Comparison Test with Trigonometric terms
🔒 Video 4: Exercise: Direct Comparison Test with rational terms 
▶ Video 5: Limit Comparison Test (LCT): Statement and 1 worked example
▶ Video 6: Exercise: Limit Comparison Test with Rational Series
🔒 Video 7 Exercise: Limit Comparison Test with Exponential Series
🔒 Video 8: Limit Comparison Test with Logarithmic terms
🔒 Video 9: Limit Comparison Test with mixed polynomial and radical terms

10.12 Lagrange Error Bound 
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▶ Video 1: Introduction to Lagrange error bound:  Free
🔒 Video 2: worked example:  Full access with subscription

10.13 Radius and Interval of Convergence of Power Series
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▶ Video 1: What is a Power Series
▶ Video 2: Possible outcomes of radius of convergence
▶ Video 3: Finding the Interval and Radius of convergence methodology
🔒 Video 4: Using Conditional Convergence to deduce the radius
🔒 Video 5: Deducing convergence from a known convergence point
🔒 Video 6: Special structures. Recognizing patterns quickly
🔒 Video 7: Reading Convergence Tables

10.14 Taylor and MacLaurin Series
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▶ Video 1: What is a Taylor and Maclaurin series?
▶ Video 2: Key series you should memorize
▶ Video 3: substitution into a known series
🔒 Video 4: Multiplying a series by a polynomial or function
🔒 Video 5: Adding or subtracting known series
🔒 Video 6: Differentiation and Integration of Series
🔒 Video 7: Extracting coefficients using the Taylor Formula
🔒 Video 8: Recognizing a Series as a known Function Value