Visual proof of the series
1 + 2r + 3r² + 4r³ + … = 1/(1-r)²
I found from @MathPrinceps
https://www.desmos.com/calculator/fnno9rplch …pic.twitter.com/37Cf9JU3RX
It's possible to do better, though -- by which I mean, to make the correspondence clearer between the terms of the series and the areas in the figure. For example, here's how I'd say it should go for r = 2/3. Note the ease of counting the thirds, the ninths, the twenty-sevenths.pic.twitter.com/qOEzqnqVHk
