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Is this true?

Cesàro means converge ⇒ the sequence converges

No — it is false.

The counterexample

Partial averages → 0, sequence diverges.

The kind of mistake this is

Converse assumed

The theorem runs one way. You used it in the other.

Drill statements like this
sequences

Others that fail the same way

From The Real Line › Sequences: convergence, monotone, Bolzano–Weierstrass, Cauchy

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