L.sufiya Khanam posted an Question
October 10, 2020 • 12:24 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Give me an example for this theorem

Theorem: If the subsequences {a and {a of a sequence {a,) converge to the same limit 1, then the sequence {a,} converges to . Proof. Let &> 0 be given

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  • Srinath best-answer

    Consider = (-1)^n/n. Here, all the a(2n + 1) terms are negative, (increasing and bounded, converges to 0), and a(2n) is positive, (decreasing and bounded, converges to 0), where 0 is the limit point of .

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