Part BCSIR NET December 2024a-discontinuous-sum-rules-out-uniform

A discontinuous sum rules out uniform

For integers n ≥ 0, let $f_{n} : [- 1, 0] \to R$ be defined by $f_{n} (x) = x / (1 - x)^{n}$ . Which of the following statements is true about the series $\sum_{(} n = 0)^{\infty} f_{n}$ ?

A.The series is neither absolutely convergent nor uniformly convergent.
B.The series is both absolutely convergent and uniformly convergent.
C.The series is absolutely convergent but not uniformly convergent.✓
D.The series is uniformly convergent but not absolutely convergent.

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: fₙ → f uniformly ⇒ fₙ′ → f′

A discontinuous sum rules out uniform

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