anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
i would try with \(\alpha =1\) first
anonymous
  • anonymous
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 \(\lim_{n\to \infty}\frac{n}{n+1}=1\)
anonymous
  • anonymous
i meant "bounded above by one" not below!

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anonymous
  • anonymous
it is monotone increasing as you can check by taking the derivative and seeing that is always positive
anonymous
  • anonymous
then try the general case with \(\alpha\)
anonymous
  • anonymous
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 \[1/(1+0)=1\] \[\alpha*1=alpha\]
anonymous
  • anonymous
the last term is alpha
anonymous
  • anonymous
the serries os monotone
anonymous
  • anonymous
the serries is also bounded below becaise it says n>1 soo first term is 1
anonymous
  • anonymous
plz give me medal if i helped

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