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Still Confused?

Try reviewing these fundamentals first

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Try reviewing these fundamentals first

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Get Started Now- Intro Lesson11:41
- Lesson: 1a16:36
- Lesson: 1b19:54
- Lesson: 1c20:29
- Lesson: 24:43

In this lesson, we will learn about the convergence and divergence of telescoping series. There is no exact formula to see if the infinite series is a telescoping series, but it is very noticeable if you start to see terms cancel out. Most telescopic series problems involve using the partial fraction decomposition before expanding it and seeing terms cancel out, so make sure you know that very well before tackling these questions.

There is no exact formula for a telescopic series.

- IntroductionTelescoping Series Overview:
- 1.
**Convergence of Telescoping Series**

Show that the following series are convergent and find its sum:

a)$\sum_{n=1}^{\infty}\frac{4}{n^2+7n+12}$b)$\sum_{n=1}^{\infty}\frac{1}{n^2+4n+3}$c)$\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$ - 2.
**Divergence of Telescoping Series with different pattern**

Show that the series $\sum_{n=1}^{\infty}(-1)^n$ is a diverging telescoping series.

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