I'm looking for an elegant visual proof the Taylor Series Expansion. It could be a picture or an animation, whichever you think would work best. The proof doesn't necessarily have to be rigorous or actually include the expansion, but I'd really like it if you could make it intuitive.


I think that there is no visual proof of taylor series or maybe very difficult, but if you need to see what happens if you add more terms of any series of a function, for example $e^x$ function

$n=0$ $$y=1$$ $n=1$ $$y=1+x$$ $n=2$ $$y=1+x+\frac{x^2}{2}$$ and so on as shown in photo

enter image description here

  • 1
    $\begingroup$ I would say "of an analytic function". $\endgroup$
    – GFauxPas
    Sep 22 '16 at 10:18
  • $\begingroup$ Thank you for the answer. That really helps you visualize what the Taylor Series is really doing. $\endgroup$ Sep 26 '16 at 3:30

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