Working with Geometric Series
Learn how to recognize, evaluate, and work with geometric series, including convergence, infinite sums, partial sums, and AP Calculus AB & BC examples.
Using Taylor Series to Approximate Function Values
Learn how to use Taylor and Maclaurin polynomials to approximate function values, choose an appropriate degree, and estimate approximation error for AP Calculus AB & BC.
The nth Term Test for Divergence
Learn how to use the nth term test for divergence to determine when an infinite series must diverge, with step-by-step examples and AP Calculus practice problems.
The Lagrange Error Bound for Taylor Polynomials
Learn how to use the Lagrange error bound to estimate the maximum error in Taylor polynomial approximations, with step-by-step AP Calculus AB & BC examples.
Testing Endpoints for Interval of Convergence
Learn how to test the endpoints of a power series to determine its full interval of convergence, with step-by-step examples for AP Calculus BC.
Taylor Polynomials: An Introduction
Learn how Taylor polynomials approximate functions using derivatives, with a step-by-step method and fully worked examples for AP Calculus BC.
Representing Functions as Power Series
Learn how to represent functions as power series using geometric series, algebraic manipulation, and differentiation and integration for AP Calculus BC.
Ratio Test for Convergence
Learn how to use the Ratio Test to determine whether an infinite series converges or diverges, with step-by-step examples and AP Calculus practice problems.
Radius and Interval of Convergence of a Power Series
Learn how to find the radius and interval of convergence of a power series, including endpoint testing, with step-by-step examples for AP Calculus BC.
Practice Problem Set: Taylor and Maclaurin Series
Practice Taylor and Maclaurin series for AP Calculus BC with problems covering common series, Taylor polynomials, intervals of convergence, error bounds, and series manipulation.