Counterexample

Is this true?

A power series converges uniformly on its open disc of convergence

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

86 counterexamples are free — including most of the ones Part C leans on hardest.

Keep practicing

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

See real exam options built on this mistake Drill statements like this

power series uniform convergence

Go deeper· Explained in full in Power series — radius, boundary, Abel· Asked in CSIR NET December 2024· From Sequences and Series of Functions › Power series, radius of convergence, Abel's theorem

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