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# Unit: Infinite sequences and series

AP Calc:
LIM (BI)
,
LIM‑7 (EU)
,
LIM‑8 (EU)
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#### 0

Possible mastery points

## Defining convergent and divergent infinite series

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

## Working with geometric series

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

#### Quiz 1

Level up on the above skills and collect up to 400 Mastery points

## The nth-term test for divergence

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!

## Integral test for convergence

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!

## Harmonic series and p-series

AP Calc:
LIM (BI)
,
LIM‑7 (EU)
,
LIM‑7.A (LO)
,
LIM‑7.A.7 (EK)
Practice
p-seriesGet 3 of 4 questions to level up!

## Comparison tests for convergence

AP Calc:
LIM (BI)
,
LIM‑7 (EU)
,
LIM‑7.A (LO)
,
LIM‑7.A.8 (EK)
,
LIM‑7.A.9 (EK)
Practice
Direct comparison testGet 3 of 4 questions to level up!
Limit comparison testGet 3 of 4 questions to level up!

## Alternating series test for convergence

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!

## Ratio test for convergence

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!

## Determining absolute or conditional convergence

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!

#### Quiz 2

Level up on the above skills and collect up to 800 Mastery points

## Alternating series error bound

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

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

## Radius and interval of convergence of power series

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)

## Representing functions as power series

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

#### Quiz 3

Level up on the above skills and collect up to 800 Mastery points
Up next for you:

#### Unit test

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

### 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.
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