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Ankur Rao Asked a Question
November 5, 2020 3:23 pmpts 30 pts
  • 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 thankyou
    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 ...
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    Deepak singh
    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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  • Mahendra devanda thankyou
    Always convergent . see the attachment
    • cropped8398651613655683353.jpg
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