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radius of convergence
"For |x-x0| = r no general statements can be made, except that there
always exists at least one complex number x with |x-x0| = r such that
the series diverges."
is clearly wrong, and should be reduced simply to
"For |x-x0| = r no general statements can be made."
As a counterexample consider the power series with general term
x^n /(n+1)^2, for which r = 1 and that converges everywhere on the
circle of convergence (it even converges absolutely).
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