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Homeradius of convergence

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# radius of convergence

The statement

"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).

Parting words from the person who closed the correction:

The statement
"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 ge

**Status:**Accepted

Reference to the user who closed the correction.:

Reference to the article this correction is about:

Status of the article (was it accepted?):

1

Status of the article (is it closed?):

1

What kind of correction is this:

Error

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