I went full @3blue1brown and used Manim to illustrate the proof of the Geometric Series formulapic.twitter.com/c3kVy63SIh
Show this thread
-
Looks great... buuuuut...sorry to be "that guy"... technically you're starting from the assumption that the series converges at all, which you do not prove with this. Similar to the "1+2+3+4+...= -1/12" argument, right?
Suppose S is finite in step 1 & there we have it the difference between this heuristic and the -1/12 one is that 1-1+1.. diverges always This converges for |r|<=1, and so while nits can be picked, at the end of the day I didn’t want to code up the condition
-
-
Yes. But you have to make that assumption, which was not visible in what you wrote or animated. iirc, the -1/12 problem goes quite a bit deeper than 1-1+1... not converging in the "for all epsilon..."sense. Indeed, I am being nit-picky, but that's math, right?
-
The heuristic doesn't go any deeper than that. All manipulations of that fashion rely on a non-traditional form of convergence(e.g. Cesaro)..I covered the proper way to consider the summation in the linked tweet yes, that's math but this is also twitterhttps://twitter.com/InertialObservr/status/1083153666431807488?s=20 …
- 3 more replies
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.