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by jonsen
6175 days ago
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You can get the proof idea from the picture: 1/4 is 1/3 of 3/4
1/4 of 1/4 is 1/3 of 3/4 of 1/4
etc.
In math: 1/4 = 1/3*3/4
1/4^2 = 1/3*3/4*1/4
1/4^3 = 1/3*3/4*1/4^2
etc.
Summing equations: (1/4^1 + 1/4^2 + ...) = 1/3 * 3/4 * (1 + 1/4^1 + 1/4^2 + ...)
<=>
(1/4^1 + 1/4^2 + ...) = 1/3 * 3/4 + 1/3 * 3/4 * (1/4^1 + 1/4^2 + ...)
<=>
x = 1/3 * 3/4 + 1/3 * 3/4 * x
<=>
x - 1/4 x = 1/4
<=>
3/4 x = 1/4
<=>
x = 4/3 * 1/4
<=>
x = 1/3
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