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graydarl Group Title

Can someone hlep me with this math problem? serie : an=(alpha*n)/(n+1), n>=1 (alpha is from R-real number). I must determine if the series is monotone and bouded thank you very much

  • 2 years ago
  • 2 years ago

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  1. satellite73 Group Title
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    i would try with \(\alpha =1\) first

    • 2 years ago
  2. satellite73 Group Title
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    in this case you would get \(a_n=\frac{n}{n+1}\) which is bounded below by \(1\) since \(\frac{n}{n+1}<1\) for all \(n\) and \(\lim_{n\to \infty}\frac{n}{n+1}=1\)

    • 2 years ago
  3. satellite73 Group Title
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    i meant "bounded above by one" not below!

    • 2 years ago
  4. satellite73 Group Title
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    it is monotone increasing as you can check by taking the derivative and seeing that is always positive

    • 2 years ago
  5. satellite73 Group Title
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    then try the general case with \(\alpha\)

    • 2 years ago
  6. Fazeelayaz Group Title
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    yes alpha* n/(n+1) limi\[\lim_{x \rightarrow \infty}{n/n+1}\] \[n/n(1+1/n)=1/(1+1/n)\] take limit to infinity \[1/(1+0)=1\] \[\alpha*1=alpha\]

    • 2 years ago
  7. Fazeelayaz Group Title
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    the last term is alpha

    • 2 years ago
  8. Fazeelayaz Group Title
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    the serries os monotone

    • 2 years ago
  9. Fazeelayaz Group Title
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    the serries is also bounded below becaise it says n>1 soo first term is 1

    • 2 years ago
  10. Fazeelayaz Group Title
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    plz give me medal if i helped

    • 2 years ago
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