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Unit: Infinite sequences and series
AP Calc:
LIM (BI)
, LIM‑7 (EU)
, LIM‑8 (EU)
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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, how we can tell whether a series converges, and how we can explore convergence in Taylor and Maclaurin series.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!
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