Problems Plus 19: Sum of Inverse Tan Series Using Exact Trig Ratios

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:
HIVE video notes: @mes/infinite-sequences-and-series-problems-plus
Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P