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Comparison & limit comparison test - Home
- AP Calculus BC
- Sequence and Series

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Calculus

Introduction to infinite seriesCalculus

P SeriesCalculus

Alternating series testCalculus

Comparison & limit comparison test Still Confused?

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Calculus

Introduction to infinite seriesCalculus

P SeriesCalculus

Alternating series testCalculus

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Get Started Now- Intro Lesson2:56
- Lesson: 1a17:38
- Lesson: 1b9:28
- Lesson: 1c11:16
- Lesson: 1d20:08
- Lesson: 216:24

In this section, we will learn about the concept of absolute and conditional convergence. We say a series is absolutely convergent if BOTH the series and absolute value of the series is convergent. If the series is convergent and the absolute value of the series is divergent, then we call that conditional convergence. First, we will be use these definitions and apply it to some of the series below. Lastly, we will look at a complicated series which requires us to convert it to a simpler form before showing if it's absolutely convergent, conditionally convergent, or divergent.

Basic concepts: Introduction to infinite series, P Series, Alternating series test, Comparison & limit comparison test ,

Let $\sum a_n$ be a convergent series. Then we say that $\sum a_n$ is **absolutely convergent** if $\sum |a_n|$ is convergent.

If $\sum |a_n|$ is divergent, then we say that $\sum a_n$ is**conditionally convergent**.

If $\sum |a_n|$ is divergent, then we say that $\sum a_n$ is

- IntroductionAbsolute & Conditional Convergence Overview
- 1.
**Questions based on Absolute & Conditional Convergence**

Determine if the series is absolutely convergent, conditionally convergent, or divergenta)$\sum_{n=2}^{\infty}\frac{(-1)^n}{n-1}$b)$\sum_{n=1}^{\infty}\frac{(-1)^n}{n^2}$c)$\sum_{n=2}^{\infty}\frac{2+cosn}{n}$d)$\sum_{n=4}^{\infty}\frac{(n^2+2)(-1)^{3n+1}}{(n^4+1)1^{n-1}}$ - 2.
**Advanced Question**

Determine if the series $\sum_{n=1}^{\infty}\frac{(-1)^{n-2}sin^2(\frac{(2n+1)\pi}{2})}{n^3}$ is absolutely convergent, conditionally convergent, or divergent.

8.

Sequence and Series

8.1

Introduction to sequences

8.2

Introduction to infinite series

8.3

Convergence and divergence of normal infinite series

8.4

Convergence and divergence of geometric series

8.5

Divergence of harmonic series

8.6

P Series

8.7

Alternating series test

8.8

Divergence test

8.9

Comparison and limit comparison test

8.10

Integral test

8.11

Ratio test

8.12

Absolute and conditional convergence

8.13

Radius and interval of convergence with power series

8.14

Functions expressed as power series

8.15

Taylor and maclaurin series

8.16

Approximating functions with Taylor polynomials and error bounds

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Get Started Now8.1

Introduction to sequences

8.3

Convergence and divergence of normal infinite series

8.4

Convergence and divergence of geometric series

8.5

Divergence of harmonic series

8.6

P Series

8.7

Alternating series test

8.8

Divergence test

8.9

Comparison and limit comparison test

8.10

Integral test

8.11

Ratio test

8.12

Absolute and conditional convergence

8.13

Radius and interval of convergence with power series

8.14

Functions expressed as power series

8.15

Taylor and maclaurin series