A community for students.
Here's the question you clicked on:
 0 viewing
graydarl
 3 years ago
I have x_n =[1/sqrt(2)+1/sqrt(3)+....+1/sqrt(n)]/sqrt(n)
I must find lim of a_n with stoltzcesaro
so [1/sqrt(2)+1/sqrt(3)+....+1/sqrt(n)]=a_n
and sqrt(n) = b_n
and in b_n > infinity i must show that lim a_n/b_n has the same limit as [a_(n+1) a_(n)]/[b_(n+1)  b_(n)]
graydarl
 3 years ago
I have x_n =[1/sqrt(2)+1/sqrt(3)+....+1/sqrt(n)]/sqrt(n) I must find lim of a_n with stoltzcesaro so [1/sqrt(2)+1/sqrt(3)+....+1/sqrt(n)]=a_n and sqrt(n) = b_n and in b_n > infinity i must show that lim a_n/b_n has the same limit as [a_(n+1) a_(n)]/[b_(n+1)  b_(n)]

This Question is Closed

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.1are you asked to prove stoltzcesaro or just apply it here? if it's the latter then just take your limit: \[\lim_{n \rightarrow \infty} \frac{ a_{n+1}  a_n }{ b_{n+1}  b_n } = \lim_{n \rightarrow \infty} \frac{\frac{1}{\sqrt{n+1}}}{\sqrt{n+1}\sqrt{n}}\] then just rationalize the denominator and you should get a pretty simple answer

graydarl
 3 years ago
Best ResponseYou've already chosen the best response.0it's good i used your lim and i got \[1 + \frac{ \sqrt{n} }{ \sqrt{n+1} }\] what can i do next this is not looking like a final form and i have a hint that the answer is two, can this be true?

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.1ugh take the limit? and the 2nd term is 1 when u do that

graydarl
 3 years ago
Best ResponseYou've already chosen the best response.0is not infinity over infinity? i am just asking i don' t know

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.1ok when n is going to infinity, that 1 in n+1 becomes negligible, so pretty much u have sqrt(n)/sqrt(n), which is just 1.

graydarl
 3 years ago
Best ResponseYou've already chosen the best response.0i understood, thank you very much :D
Ask your own question
Sign UpFind more explanations on OpenStudy
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.