A community for students.
Here's the question you clicked on:
 0 viewing
bahrom7893
 4 years ago
Sequences and series
bahrom7893
 4 years ago
Sequences and series

This Question is Closed

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3this one and one more left.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1we know know that \[\int_{1}^{n}\frac{1}{x}dx=\ln(n)\] ...

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1330845983664:dw the sum of the rectangles is the sum of 1/x which is larger than the area under the curve which is the integral thus \[\sum_{k=1}^{n}\frac{1}{k}>\ln(n)\] ie.. \[\sum_{k=1}^{n}\frac{1}{k}\ln(n)>0\]

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3TY TY TY TY TY Zarkon.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1\[\int_{n}^{n+1}\frac{1}{x}dx=\ln(n+1)\ln(n)\] dw:1330846312070:dw the area of this rectangle is 1*(n+1)=n+1 and it is less than the area under the curve...thus... \[\frac{1}{n+1}<\ln(n+1)\ln(n)\] \[\frac{1}{n+1}\ln(n+1)<\ln(n)\] \[\sum_{k=1}^{n}\frac{1}{n}+\frac{1}{n+1}\ln(n+1)<\sum_{k=1}^{n}\frac{1}{n}\ln(n)\] \[a_{n+1}<a_{n}\]

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1for part c since \(a_n>0\) and \(a_{n+1}<a_n\) by the monotone bounded sequence theorem \(a_n\) converges.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1use you calculator or computer to get part (d)

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3TY SOO MUCH! One more problem left for today.. I hope, unless i get stuck on computational ones.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1it is getting really late here so it needs to be quick if you want my help

bahrom7893
 4 years ago
Best ResponseYou've already chosen the best response.3ok sure one more and that's it then.
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.