Name: Problems Plus 16: The Number e Defined as a Recursive Series
Uploaded: 2023-09-28T05:00:04+00:00
Duration: 15 min 13 s
Description: In this video I go over a pretty amazing math problem on finding the sum of a series that is defined by a simple recursive formula, and it somehow turns out to be the number e! A recursive function is

2 years ago

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math science stem education number e series sequences and series amazing math mes

In this video I go over a pretty amazing math problem on finding the sum of a series that is defined by a simple recursive formula, and it somehow turns out to be the number e! A recursive function is such that it depends on a previous version of itself, hence each new iteration modifies the previous value before it. In this problem, a sequence is defined recursively and by using the principle of mathematical induction, I show that as the series approaches an infinite number of terms the sum of the series approaches the number e. Truly amazing stuff!

The timestamps of key parts of the video are listed below:

- Problem 16: Recursive Sequence: 0:00
- Solution: 0:56
- Mathematical induction: 6:45
- Solving for the general case: 7:52
- Series is equal to the number e: 14:05

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P