- Home
- Calculus 2
- Sequence and Series
Convergence & divergence of telescoping series
- Intro Lesson11:41
- Lesson: 1a16:36
- Lesson: 1b19:54
- Lesson: 1c20:29
- Lesson: 24:43
Convergence & divergence of telescoping series
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.
Lessons
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)∑n=1∞n2+7n+124b)∑n=1∞n2+4n+31c)∑n=1∞4n2−11 - 2.Divergence of Telescoping Series with different pattern
Show that the series ∑n=1∞(−1)n is a diverging telescoping series.
Do better in math today
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
Don't just watch, practice makes perfect
Practice topics for Sequence and Series
5.1
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