Main content

# Infinite sequences and series

AP Calc: LIM (BI), LIM‑7 (EU), LIM‑8 (EU)

AP Calc: LIM (BI), LIM‑7 (EU), LIM‑7.A (LO), LIM‑7.A.1 (EK), LIM‑7.A.2 (EK)

Learn

Practice

Sequence convergence/divergenceGet 3 of 4 questions to level up!

Partial sums introGet 3 of 4 questions to level up!

Partial sums & seriesGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑7 (EU), LIM‑7.A (LO), LIM‑7.A.3 (EK), LIM‑7.A.4 (EK)

Learn

Practice

Infinite geometric seriesGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑7 (EU), LIM‑7.A (LO), LIM‑7.A.5 (EK)

Practice

nth term testGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑7 (EU), LIM‑7.A (LO), LIM‑7.A.6 (EK)

Practice

Integral testGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑7 (EU), LIM‑7.A (LO), LIM‑7.A.7 (EK)

Learn

Practice

p-seriesGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑7 (EU), LIM‑7.A (LO), LIM‑7.A.8 (EK), LIM‑7.A.9 (EK)

Learn

Practice

Direct comparison testGet 3 of 4 questions to level up!

Limit comparison testGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑7 (EU), LIM‑7.A (LO), LIM‑7.A.10 (EK)

Practice

Alternating series testGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑7 (EU), LIM‑7.A (LO), LIM‑7.A.11 (EK)

Practice

Ratio testGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑7 (EU), LIM‑7.A (LO), LIM‑7.A.12 (EK), LIM‑7.A.13 (EK)

Practice

Determine absolute or conditional convergenceGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑7 (EU), LIM‑7.B (LO), LIM‑7.B.1 (EK)

Learn

Practice

Alternating series remainderGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑8 (EU), LIM‑8.A (LO), LIM‑8.A.1 (EK), LIM‑8.A.2 (EK), LIM‑8.B (LO), LIM‑8.B.1 (EK)

Learn

Practice

Taylor & Maclaurin polynomialsGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑8 (EU), LIM‑8.C (LO), LIM‑8.C.1 (EK)

Learn

Practice

Lagrange error boundGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑8 (EU), LIM‑8.D (LO), LIM‑8.D.1 (EK), LIM‑8.D.2 (EK), LIM‑8.D.3 (EK), LIM‑8.D.4 (EK)

Practice

Interval of convergenceGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑8 (EU), LIM‑8.E (LO), LIM‑8.E.1 (EK), LIM‑8.F (LO), LIM‑8.F.1 (EK), LIM‑8.F.2 (EK)

Learn

Practice

Function as a geometric seriesGet 3 of 4 questions to level up!

Maclaurin series of sin(x), cos(x), and eˣGet 3 of 4 questions to level up!

AP Calc: LIM (BI), LIM‑8 (EU), LIM‑8.D (LO), LIM‑8.D.6 (EK), LIM‑8.G (LO), LIM‑8.G.1 (EK)

Learn

Practice

Integrate & differentiate power seriesGet 3 of 4 questions to level up!

Integrals & derivatives of functions with known power seriesGet 3 of 4 questions to level up!

Learn

### About this unit

Series are sums of multiple terms. Infinite series are sums of an infinite number of terms. Don't all infinite series grow to infinity? It turns out the answer is no. Some infinite series converge to a finite value. Learn how this is possible and how we can tell whether a series converges and to what value. We will also learn about Taylor and Maclaurin series, which are series that act as functions and converge to common functions like sin(x) or eˣ.AP® is a registered trademark of the College Board, which has not reviewed this resource.