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Counterexample

Is this true?

∑an\sum{}a_{n} convergent ⇒∑an2\Rightarrow \sum{}a_{n}^{2} convergent

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

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

Go deeper· Explained in full in Series tests — decision tree and the trap list· Asked in CSIR NET December 2025· From The Real Line › Series: comparison, ratio, root, Raabe, condensation, alternating, rearrangements

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