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# Unit: Infinite sequences and series

AP Calc:

LIM (BI)

, LIM‑7 (EU)

, LIM‑8 (EU)

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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!

Level up on the above skills and collect up to 320 Mastery points

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!

Level up on the above skills and collect up to 640 Mastery points

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!

Level up on the above skills and collect up to 640 Mastery points

### Learn

Up next for you:

Level up on all the skills in this unit and collect up to 2000 Mastery points!#### Unit test

### 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.