I love these little tricky recursive proofs but won't ask you about this equality in the case x = 0.
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dont you mean x =1 ? ;)
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This is true only for x < 1, right?
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that's right for |x|<1
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I remember being stunned by this back in high school.
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It's magic. S gives birth to itself and more. Then redefines itself in terms of more.
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An oldie but a goodie.
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After showing this, I love to let my students try the same thing for 1+2+4+8+... and let the fireworks go off.
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Iff |x|<1
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