3.140001000000000000000005... (Transcenedental numbers question!).?
Just like 0.11000100000000000000000100... where a digit is 1 in the nth factorial place is equal to the series 10^(-1!) + 10^(-2!) + 10^(-3!) +..., what is the infinite series for 3.140001000000000000000005... where in the nth factorial place there is the nth digit of the decimal expansion of pi. I hope you understand what i'm asking. Thank you for your answer!
Update:http://en.wikipedia.org/wiki/Liouville_number
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If I'm understanding this correctly, I think the series you're looking for is defined by:
s_n = 10^(-n!)( [[pi*10^n]] - [[10pi*10^(n - 1)]] )
Right now I can't think of a simpler way to express it, so I'm using the floor function, defined by f: R --> N, f(r) = [[r]] max({n in N | n <= r < n+1})