Is this the Coolest Approximation for e?

In 2004 Eric Friedman issued a challenge - to find the best approximation for some famous irrational numbers using the first n digits. Among these numbers was, of course, Euler's number e. One brave challenger, Richard Sabey, had an incredible showing - giving us an amazing approximation of e, accurate to over 18 septillion digits, using the digits 1-9. We explore the approximation today, and how to determine its accuracy without computing the massive numbers involved. This involved discussing the limit definition of e, as well as compound interest and power series. #maths #mathematics #math I just launched a math fashion brand at https://mathshion.com/ Check it out and pick up some of the coolest math merch of all time! Join Wrath of Math to get exclusive videos, lecture notes, and more: https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join SOURCES Eric's original problem page: https://erich-friedman.github.io/mathmagic/0804.html https://mathworld.wolfram.com/eApproximations.html https://math.stackexchange.com/questions/1945026/an-amazing-approximation-of-e https://www.johndcook.com/blog/2014/03/30/amazing-approximation-to-e/ https://en.wikipedia.org/wiki/Pandigital_number Stewart, J. (2012). Calculus : early transcendentals. Belmont, Cal.: Brooks/Cole, Cengage Learning. 0:00 Intro 1:03 e Approximations 1:53 Friedman's Challenge 4:39 Sabey's Pandigital Approximation 5:33 The Issue 9:47 Rewriting 12:39 Showing the log is Near 1