Richard P. answered • 11/03/13

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ln(1+z) = Σn=1,∞ (-1)

^{n-1}z^{n}/n sog(x) = ∑n=1,∞ (-1)

^{n-1}x^{2(n-1)}/nTo get an idea about the radius of curvature, consider what happens for purely imaginary values of x,that is let x = i b for real b.

g(i b) = ∑n=1,∞ b

^{2(n-1)}/n for b = 1 this series diverges logarithmically. for b >1 the divergence is even faster.So the radius of curvature is |x| <1

Andre W.

11/03/13