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Topic: Is the C of Euler an irrational number?
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Luis A. Rodriguez

Posts: 732
Registered: 12/13/04
Is the C of Euler an irrational number?
Posted: Oct 11, 2012 7:00 AM
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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



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