Geometric explanation as to why $\sum_{n=1}^\infty \frac{1}{x^n}$ converges to $\frac{1}{x-1}$?

Asked May 01 '18 at 15:31

Active May 01 '18 at 15:31

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Is there any simple, preferrably geometric, explanation as to why the sum $$\sum_{n=1}^\infty \frac{1}{x^n}$$ converges to $\frac{1}{x-1}$ ?

asked May 01 '18 at 15:31

https://en.wikipedia.org/wiki/Geometric_series has a few pictures – tired May 01 '18 at 15:38
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https://math.stackexchange.com/questions/483575/question-on-geometrical-proof-of-geometric. Ok? – Peter Szilas May 01 '18 at 15:48
g3nuine.Looks like a nice proof. :)) – Peter Szilas May 01 '18 at 17:06
@PeterSzilas Youre right, its a really nice explanation, sadly I cant accept your comment as answer – SmallestUncomputableNumber May 02 '18 at 01:09
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g3nuine.No worry, thanks for your kind words, Peter – Peter Szilas May 02 '18 at 07:10

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