Ankur posted an Question
November 05, 2020 • 20:53 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Let series un is convergent and vn is bounded sequence then series unvn is convergent or not

let series Un is convergent and Vn is bounded sequence then series UnVn is convergent or not

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    Deepak singh 1 best-answer

    correct statement - if series Un is convergent and and sequence Vn is monotonic and bounded then series Un.Vn is convergent ... Notice that here Vn should be monotonic also if any doubt then reply

    eduncle-logo-app

    if Vn is not monotonic then series Un.Vn may not be convergent..

  • Srinath

    Consider the series un to be (-1)^n/n. Let vn be the bounded sequence (-1)^n. Observe that, the series unvn is not convergent.

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