Calculus 2, Series Convergence Questions?

Click For Summary

Homework Help Overview

The discussion revolves around problems related to series and convergence in a Calculus 2 context. Participants are exploring various convergence tests, particularly the ratio test and p-test, while addressing specific series involving trigonometric functions.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply the ratio test to determine convergence but expresses difficulty in understanding the concepts. They also mention challenges with alternating series.
  • One participant questions the convergence of a specific series, sin(3n)/n^2, suggesting a comparison to 1/n^2 and referencing the p-test for absolute convergence.
  • Another participant confirms the original poster's assessment of the series but does not elaborate on the reasoning.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on specific series and convergence tests. Some guidance has been offered regarding the convergence of the problematic series, but there is no clear consensus on the overall correctness of the original poster's attempts.

Contextual Notes

The original poster is under time constraints, as the problems are due soon, which may be influencing their urgency and approach to seeking help.

MMhawk607
Messages
5
Reaction score
0
I have some problems here with Series and Convergence...

Here are the problems and my guesses at it.

http://img822.imageshack.us/img822/9523/23341530.png

It won't tell me which one is wrong, but it just says one/all is wrong. Any help is appreciated.

Attempts at solving, I tried using ratio test for these but I can't seem to get it. I need more comprehension of these types of problems I know, but these problems are due by tonight.
Alternating series really give me trouble too.
 
Last edited by a moderator:
Physics news on Phys.org
OH

It was because of the third problem

sin(3n)/n^2

Is it because

sin(3n) / (n^2) ≤ 1/(n^2)

Therefore the p test makes it absolutely convergent?

I had the other 4 right, I figured that one was A though, is this the reason?
 
MMhawk607 said:
OH

It was because of the third problem

sin(3n)/n^2

Is it because

sin(3n) / (n^2) ≤ 1/(n^2)

Therefore the p test makes it absolutely convergent?

I had the other 4 right, I figured that one was A though, is this the reason?
Hello MMhawk607. Welcome to PF !

Yes, you had #3 wrong .

It is absolutely convergent.
 
mmhawk607 said:
i have some problems here with series and convergence...

Here are the problems and my guesses at it.

http://img822.imageshack.us/img822/9523/23341530.png

it won't tell me which one is wrong, but it just says one/all is wrong. Any help is appreciated.

Attempts at solving, i tried using ratio test for these but i can't seem to get it. I need more comprehension of these types of problems i know, but these problems are due by tonight.
Alternating series really give me trouble too.
...                         .
 
Last edited by a moderator:

Similar threads

Valid conclusion for an absolutely convergent sequence
  • · Replies 4 ·
Replies
4
Views
1K
Proving convergence and divergence of series
  • · Replies 3 ·
Replies
3
Views
2K
Does this series converge uniformly?
  • · Replies 7 ·
Replies
7
Views
2K
Determining if a series converges
  • · Replies 4 ·
Replies
4
Views
2K
Studying the convergence of a series with an arctangent of a partial sum
  • · Replies 7 ·
Replies
7
Views
2K
How to show that these sequences are summable?
  • · Replies 1 ·
Replies
1
Views
2K
Proving the convergence of series
  • · Replies 14 ·
Replies
14
Views
2K
Intervals of Convergence- Power Series
  • · Replies 11 ·
Replies
11
Views
3K
Show that the series ##\sum_{n=2}^\infty\dfrac {1}{n^2\ln (n)}##converges
  • · Replies 51 ·
2
Replies
51
Views
7K
Series: Determine if they are convergent or divergent
  • · Replies 22 ·
Replies
22
Views
3K