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Comparison & limit comparison test - Home
- Integral Calculus
- Sequence and Series

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Calculus

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Calculus

Introduction to infinite seriesCalculus

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Get Started Now- Lesson: 12:56
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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

- 1.Absolute & Conditional Convergence Overview
- 2.
**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)$\sum_{n=4}^{\infty}\frac{(n^2+2)(-1)^{3n+1}}{(n^4+1)1^{n-1}}$ - 3.
**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.

5.

Sequence and Series

5.1

Introduction to sequences

5.2

Monotonic and bounded sequences

5.3

Introduction to infinite series

5.4

Convergence and divergence of normal infinite series

5.5

Convergence & divergence of geometric series

5.6

Convergence & divergence of telescoping series

5.7

Divergence of harmonic series

5.8

P Series

5.9

Alternating series test

5.10

Divergence test

5.11

Comparison & limit comparison test

5.12

Integral test

5.13

Ratio test

5.14

Root test

5.15

Absolute & conditional convergence

5.16

Radius and interval of convergence with power series

5.17

Functions expressed as power series

5.18

Taylor series and Maclaurin series

5.19

Approximating functions with Taylor polynomials and error bounds

We have over 170 practice questions in Integral Calculus for you to master.

Get Started Now5.1

Introduction to sequences

5.2

Monotonic and bounded sequences

5.4

Convergence and divergence of normal infinite series

5.5

Convergence & divergence of geometric series

5.6

Convergence & divergence of telescoping series

5.7

Divergence of harmonic series

5.8

P Series

5.9

Alternating series test

5.10

Divergence test

5.11

Comparison & limit comparison test

5.12

Integral test

5.13

Ratio test

5.14

Root test

5.15

Absolute & conditional convergence

5.16

Radius and interval of convergence with power series

5.17

Functions expressed as power series

5.18

Taylor series and Maclaurin series