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Is the C of Euler an irrational number?
Posted:
Oct 11, 2012 7:00 AM


Be H(n) = Sum {1/i ; i = 1 to n} Calling R(n) = 1/2n + 1/12n^2.(1  1/10n^2 + 1/20n^4....) By definition C = H(n)  Log(n) + R(n)
If n = 3 > C = 11/6  Log(3) + R(3) But Log(3) is irrational and Log(3) = 2[1/2 + 1/3.2^3 + 1/5.2^5 + 1/7.2^7....]
The only form for obtaining R(3)  Log(3) as a rational number is that R(3)= rational + Log(3). But that is impossible because R(3) cannot contain Log(3) inasmuch as R(3) = 1/6 + 1/108( 1  1 / 10.3^2 + 1 / 20.3^4...)
Is this a valid demonstration? Ludovicus



