Series investigation: divergence/convergence

Click For Summary
SUMMARY

The forum discussion centers on the convergence and divergence of the series represented by the equation $$\sum_{k=1}^{\infty}\frac{k^3}{(k^2+2)^2}$$. Participants confirm the correctness of the calculations and emphasize the importance of using LaTeX for presenting mathematical expressions. Users are guided on how to access the LaTeX features within the forum, including a "LaTeX Guide" link for further assistance. The conversation highlights the collaborative nature of problem-solving in mathematical discussions.

PREREQUISITES
  • Understanding of series convergence and divergence concepts
  • Familiarity with LaTeX for typesetting mathematical equations
  • Basic knowledge of calculus and infinite series
  • Experience using online forums for academic discussions
NEXT STEPS
  • Learn how to use LaTeX for mathematical expressions
  • Study convergence tests such as the Ratio Test and Root Test
  • Explore advanced series topics, including power series and Taylor series
  • Participate in online forums focused on mathematics for collaborative learning
USEFUL FOR

Students, educators, and mathematics enthusiasts seeking to enhance their understanding of series convergence and divergence, as well as those looking to improve their LaTeX skills for mathematical documentation.

physicisttobe
Messages
56
Reaction score
13
Homework Statement
Series (convergence/divergence)
Relevant Equations
....
Hi everyone!
It's about the following task: show the convergence or divergence of the following series (combine estimates and
criteria).

I am not sure if I have solved the problem correctly. Can you guys help me? Is there anything I need to correct? I look forward to your feedback.
89FB95E5-A4D2-4861-AF3B-DB0C37F79752.jpeg
 
Reply
  • Like
Likes   Reactions: nuuskur and FactChecker
Physics news on Phys.org
Looks fine. If you want to post more problems you may want to learn Latex. See the help pages.
 
Reply
  • Like
Likes   Reactions: vela
For example:
$$\sum_{k=1}^{\infty}\frac{k^3}{(k^2+2)^2}$$
 
Thank you for your response PeroK! So everything was calculated correct, right?
And yes, I'll try Latex. But how do I have to proceed? I don't find the button for Latex in this forum.
 
physicisttobe said:
Thank you for your response PeroK! So everything was calculated correct, right?
And yes, I'll try Latex. But how do I have to proceed? I don't find the button for Latex in this forum.
You just type it in. The icon on the top right gives you a preview.
 
physicisttobe said:
And yes, I'll try Latex. But how do I have to proceed? I don't find the button for Latex in this forum.
Thank you for learning to post equations using LaTeX. You can click the "LaTeX Guide" link below the Edit window to learn more. :smile:
 
You can also quote a post to see what they did to get latex in their post.
 
Last edited by a moderator:
Reply
  • Like
Likes   Reactions: berkeman
Hi berkeman!
I can't find the Latex Guide. Where is the edit window? I'm quite new in this forum.

Edit: Okay, I found it right now :biggrin: thank you
 
Are you on a phone or your laptop? On a laptop with Firefox browser, I see this:

1669054488079.png
 

Similar threads

Proving convergence and divergence of series
  • · Replies 3 ·
Replies
3
Views
2K
Determining if a series converges
  • · Replies 4 ·
Replies
4
Views
2K
On the definition of radius of convergence; a small supremum technicality
  • · Replies 7 ·
Replies
7
Views
2K
Ratio Test vs AST
  • · Replies 4 ·
Replies
4
Views
1K
Is Using the Comparison Test to Prove Divergence Valid for This Series?
  • · Replies 29 ·
Replies
29
Views
2K
Absolute convergence of series
  • · Replies 2 ·
Replies
2
Views
1K
Intervals of Convergence- Power Series
  • · Replies 11 ·
Replies
11
Views
3K
Is the Interval of Convergence for (x-2)^n / n^(3n) from -1 to 5?
  • · Replies 2 ·
Replies
2
Views
1K
Test the following series for convergence or divergence
  • · Replies 7 ·
Replies
7
Views
2K
Proving the convergence of series
  • · Replies 14 ·
Replies
14
Views
2K