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- Sequence and Series

Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

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Get Started Now- Intro Lesson3:27
- Lesson: 1a3:12
- Lesson: 1b4:04
- Lesson: 1c5:23
- Lesson: 27:55

In this lesson, we will learn about the divergence test. The test states that if you take the limit of the general term of the series and it does not equal to 0, then the series diverge. Keep in mind that if you do take the limit and it goes to 0, that does not mean the series is convergent. It only means the test has failed, and you will have to use another method to find the convergence or divergence of the series. It is recommended to use the divergence test if u can obviously see that the limit of the general term goes to infinity. For the first few questions, we will see if the divergence test applies to the series. For the last question, we will see if the series is convergent or divergent by using the test.

Basic concepts: Introduction to infinite series, Convergence and divergence of normal infinite series ,

Note *The divergence test states the following:

If $\lim$_{n →$\infty$} $a$_{$n$} $\neq$ 0, then the series $\sum a_n$ diverges.

If $\lim$

- IntroductionDivergence Test Overview
- 1.
**Understanding of the Divergence Test**

Does the divergence test work for the following series?

a)$\sum_{n=1}^{\infty}\frac{10}{n}$b)$\sum_{n=4}^{\infty}\frac{n^2+n^3}{n^3+1}$c)$\sum_{n=2}^{\infty}\frac{n-1}{ln(n)}$ - 2.
**Advanced Question Regarding to the Divergence Test**

Determine if the series $\sum_{k=1}^{\infty}k^{-\frac{1}{k^3}}$ converges or diverges.

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 Calculus 2 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