← All units AP Calculus BC · Unit 10
AP Calculus BC · Unit 10 · Infinite Sequences & Series

Infinite series, made visual.

The hardest unit in BC, rebuilt as something you can see. Six interactive tools that turn convergence, Taylor series, and error bounds from symbols on a page into things that move.

15Topics covered
6Interactive tools
Series, demystified
Explore the tools

The toolkit

Work them in order for a full walkthrough of the unit, or jump straight to whatever's giving you trouble.

10.1 – 10.3

Series Foundations

What a series even is, and what it means for an infinite sum to "add up." Watch the partial sums climb to a limit — or run off forever — one term at a time.

sequences vs seriespartial sumsconvergencethe harmonic trap
Open
10.4 – 10.9

Convergence Compass

Nine tests, and the real skill is knowing which to reach for. Meet each test, compare them at a glance, then drill until you can name them on sight.

all 9 testscheat sheetpractice quizworked solutions
Open
10.10, 10.12

Error Bounds

Stop adding terms — how wrong are you? Watch the error shrink under its guaranteed bound, then master both the alternating-series bound and the dreaded Lagrange error bound.

alternating boundLagrange errorremainderRₙ ≤ bound
Open
10.13

Interval of Convergence

A power series only converges near its center. See the interval on a number line, find the radius with the ratio test, and nail the endpoint check everyone forgets.

power seriesradiusratio testendpoint check
Open
10.11, 10.14 – 10.15

Taylor Toolkit

Watch any function get rebuilt out of powers of x, one term at a time — then see where the approximation holds and where it breaks down. Taylor & Maclaurin series, made tangible.

Taylor seriesMaclaurinconvergence radiuserror band
Open

The capstone

Put it all together the way the real exam does — mixed review first, then full free-response.

Exam Practice

Mixed multiple choice & full free-response

You pick the approach: mixed multiple choice across all fifteen topics with deep explanations and a weak-spot finder, plus chained free-response built in the real Question 6 mold.

Begin practicing
Cheat Sheet — every test, every series, and the "which test?" logic on one printable page

The full unit, plus exam practice

From what a series is, through the nine convergence tests and Taylor series, to power-series intervals and error bounds — and a capstone that mixes it all together the way the real exam does. Everything verified, nothing hand-wavy.

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