Exercise 2: Sum of diameters of Infinite Circles
In this video, I show that the sum of diameters of an infinite number of circles contacting between two big circles sums to the radius of the bigger circles, thus providing a geometric interpretation of the series with terms 1/(n(n + 1)). I first use the trigonometric identity to obtain an equation involving the diameter of the smaller circles, and then use mathematical induction (as well as my previous telescoping sum result) to show that the diameter of subsequent small circles is identical to the series terms.
3Speak - YouTube - Telegram - Notes - Playlist - Sequences and Series - MES Links
Leave Exercise 2: Sum of diameters of Infinite Circles to:
Best Posts From Math Easy Solutions
We have not curated any of mes's posts yet. But you can encourage our curation team to review posts by visiting them regularly and by referring other readers. Because we give priority to frequently read content.
More Posts From Math Easy Solutions
- Exercise 2: Sum of diameters of Infinite Circles
- Exercise 2: Sum of diameters of Infinite Circles
- Grok
- Michael Faraday
- Dr. Mahmoud Hessabi
- Exercise 1: Sum of differences between curves y = x^n as an infinite series
- Exercise 1: Sum of differences between curves y = x^n as an infinite series
- 3.11 Telltale moondust
- 3.10 Japan’s 3D Moon maps
- Ultrahigh-definition volumetric light field projection