In this video I'll talk about Ramanujan's infinite roots problem, give the solution to my infinite continued fraction puzzle from a couple of week's ago, and let you in on the tricks of the trade when it comes to making sense of all those crazy infinite expressions. Featuring guest appearances by Vihart's infinite Wau fraction, the golden ratio and the Mandelbrot set. Here is a link to a screenshot of Ramanujan’s original note about his infinite nested radical puzzle: http://www.qedcat.com/misc/ram_incomplete.jpg Check out the following videos referred to in this video: https://www.youtube.com/watch?v=jcKRGpMiVTw Mathologer video on Ramanujan and 1+2+3+...=-1/12. This one also features an extended discussion of assigning values to infinite series in the standard and a couple of non-standard ways https://www.youtube.com/watch?v=CaasbfdJdJg Mathologer video on infinite fractions and the most irrational of all irrational numbers. https://www.youtube.com/watch?v=9gk_8mQuerg Mathologer video on the Mandelbrot set. The second part of this one is all about a supernice way of visualising the infinite expression at the heart of this superstar. https://www.youtube.com/watch?v=GFLkou8NvJo Vi Hart's video on the mysterious number Wau, a must-see :) Enjoy :)