Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
graydarl
Group Title
Can someone hlep me with this math problem? serie : an=(alpha*n)/(n+1), n>=1 (alpha is from Rreal number). I must determine if the series is monotone and bouded thank you very much
 2 years ago
 2 years ago
graydarl Group Title
Can someone hlep me with this math problem? serie : an=(alpha*n)/(n+1), n>=1 (alpha is from Rreal number). I must determine if the series is monotone and bouded thank you very much
 2 years ago
 2 years ago

This Question is Closed

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
i would try with \(\alpha =1\) first
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
i meant "bounded above by one" not below!
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
it is monotone increasing as you can check by taking the derivative and seeing that is always positive
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
then try the general case with \(\alpha\)
 2 years ago

Fazeelayaz Group TitleBest ResponseYou've already chosen the best response.0
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

Fazeelayaz Group TitleBest ResponseYou've already chosen the best response.0
the last term is alpha
 2 years ago

Fazeelayaz Group TitleBest ResponseYou've already chosen the best response.0
the serries os monotone
 2 years ago

Fazeelayaz Group TitleBest ResponseYou've already chosen the best response.0
the serries is also bounded below becaise it says n>1 soo first term is 1
 2 years ago

Fazeelayaz Group TitleBest ResponseYou've already chosen the best response.0
plz give me medal if i helped
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.