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In this video I go over a pretty extensive tutorial on infinite series, its definition, and many examples to elaborate in great detail. An infinite series is the summation of a sequence of terms as the terms approach an infinite number of terms and follow from my earlier video on infinite sequences; thus much of the previous video applies to this video. Several important series are covered such as the Geometric series and the Harmonic Series covered. Also, several interesting derivation techniques are utilized such as partial fraction decomposition and the amazing telescoping sum concept. I go over many examples and 2 important exercises from my calculus book (Early Transcendentals by James Stewart) to make the concept of infinite series, and their divergence or convergence, much more clear.

The topics and sections covered in this video are listed below with their timestamps:

- @ 1:34 - Infinite Series and Notation
- @ 8:29 - Definition 1

- @ 13:11 - Example 1: Geometric Series
- @ 27:43 - Example 2
- @ 32:49 - Example 3
- @ 39:49 - Example 4
- @ 48:28 - Example 5

- @ 51:10 - Example 6: Telescoping Sum
- @ 1:01:31 - Example 7: Harmonic Series
- @ 1:10:30 - Theorem 1
- @ 1:16:02 - Test for Divergence
- @ 1:17:30 - Example 8

- @ 1:20:35 - Theorem 2
- @ 1:28:15 - Example 9

- End of Chapter Exercises
- @ 1:35:10 - Exercise 1
- @ 1:45:43 - Exercise 2

Download the notes in my video:

PDF Notes: https://1drv.ms/b/s!As32ynv0LoaIh8gxUmX71Fk9dZ5_wg

Excel File: https://1drv.ms/x/s!As32ynv0LoaIh8gwtUIvFFz4HKE0DA

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/infinite-series-definition-examples-geometric-series-harmonics-series-telescoping-sum-more

Related Videos:

Infinite Sequences: Limits, Squeeze Theorem, Fibonacci Sequence & Golden Ratio + MORE: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more

Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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