A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
determine whether this series converges or diverges sigma 1 to infinity 1^(n1)2^n/(n^2)
anonymous
 5 years ago
determine whether this series converges or diverges sigma 1 to infinity 1^(n1)2^n/(n^2)

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0These fractional types usually suggest ratio test

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sum_{n=1}^{\infty}\frac{(1)^{n1} 2^n}{n^2}\] as chag said, using the ratio test, you'll get: \[\frac{an+1}{an} = \frac{(1)^n2^{n+1}}{(n+1)^2} . \frac{n^2}{(1)^{n1}2^n}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[= \frac{2^n.2^1}{(n+1)^2} . \frac{n^2}{2^n} = \frac{2n^2}{(n+1)^2}\] now the second step is to find the limit as n> infinity: \[\lim_{n \rightarrow \infty} \frac{2n^2}{(n+1)^2} = 2\] and the Ratio Test's theorem says the following: if L (limit) > 1 = series diverge if L <1 = series converge if L = 1 , no conclusion Correct me if I'm wrong please ^_^

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so for this case, since 2 > 1, then the following series diverge :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you don't understand what I did, let me know :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can u help me with another problem

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'll give it a try ^_^
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.