Name: Problems Plus 20: Sum of Infinite Series Equals ln 2. Amazing!
Uploaded: 2023-10-06T04:00:06+00:00
Duration: 26 min 46 s
Description: In this video I go over a pretty amazing infinite series and show, after an extensive math proof, that it equals to ln 2. The series is sum of the infinite terms that follow the pattern 1/(1*2) + 1/(3

2 years ago

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Health & Science Education math calculus science stem series infinite series natural log stewart calculus mathematics

In this video I go over a pretty amazing infinite series and show, after an extensive math proof, that it equals to ln 2. The series is sum of the infinite terms that follow the pattern 1/(1*2) + 1/(3*4) + 1/(5*6) + ... etc., and somehow this equals to the simple answer of ln 2 or natural log of 2. While the proof is complicated, fortunately the problem has 4 parts to provide the steps to solving for the proof. The steps involve writing a geometric series as an integral and then determining an inequality from solving the definite integral from x = 0 to x = 2 which includes ln 2 in the result. Rearranging the inequality and we obtain our final answer of ln 2. Amazing stuff!

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

- Problem 20: 0:00
- Solution to (a): 1:48
- Solution to (b): 6:55
- Solution to (c): 11:54
- Solution to (d): 20:44
- Final answer: Sum of series is ln 2: 25:52

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