But that's just (1/x) Exp[Ln[x]] = (1/x) * x = 1. Not very spooky.
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I did. This expression is just (1/x) times the Maclaurin series of Exp[y] where y = Ln[x], i.e., x / x. It's cute, but not spooky.
The thing that I spooked me at first was the fact we have an uncountable number of series that all converge to 1.. not so much about *how* but more about how at infinity these terms all add up to the same number
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Due to composition of inverse functions. The derivative of your series wrt x is 0.
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