Name: Problems Plus 19: Sum of Inverse Tan Series Using Exact Trig Ratios
Uploaded: 2023-10-03T04:13:38+00:00
Duration: 13 min 45 s
Description: In this video I go over the sum of an infinite series that can be solved by noting it is just the Maclaurin series for inverse tan for the angle π/6. Using exact trigonometric ratios, by splitting an

2 years ago

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math education calculus science stem series sequences trig trigonmetric trigonometric functions trigonometry

In this video I go over the sum of an infinite series that can be solved by noting it is just the Maclaurin series for inverse tan for the angle π/6. Using exact trigonometric ratios, by splitting an equilateral triangle and applying the Pythagorean Theorem, I show that tan(π/6) = 1/sqrt(3). This means that the inverse tan or arctan(1/sqrt(3)) = π/6. Plugging this value into our earlier Maclaurin series for tan(x), we obtain a formula that includes are given series in the Problem, which we can solve fairly easily.

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

- Problem 19: 0:00
- Solution: Maclaurin series for arctan(x): 0:19
- Exact trig ratios triangle for tan(π/6) 2:45
- Series for arctan(1/sqrt(3)): 5:19
- Alternate form of the solution: 12:40

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