Determine whether the sequence converges or diverges and find the limit

  • Thread starter Thread starter Sean1218
  • Start date Start date
  • Tags Tags
    Limit Sequence
Click For Summary

Homework Help Overview

The problem involves determining the convergence or divergence of a sequence defined as an = 11/n² + 21/n² + ... + n1/n². Participants are tasked with finding the limit if it converges.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster expresses uncertainty about simplifying the terms in the sequence and questions the relevance of introducing a variable from Riemann Sums. Other participants suggest factoring out terms and writing an expression for the sum of integers, prompting further clarification on these suggestions.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the sequence and its components. Some guidance has been offered regarding factoring and summation, but there is no explicit consensus on the approach to take.

Contextual Notes

There appears to be confusion regarding the simplification of terms and the application of Riemann sums, which may affect the understanding of the problem. The original poster's uncertainty about the suggested methods indicates a need for further clarification.

Sean1218
Messages
84
Reaction score
0

Homework Statement



Determine whether the sequence an = 11/n2 = 21/n2 + ... + n1/n2 converges or diverges. If it converges, find the limit.

2. The attempt at a solution

I have no idea what to do with this problem. I don't see why I can't simplify n/n^2 to 1/n. It was suggested to me to factor out 1/n and introduce the variable i (from Riemann Sums), but I don't see how that helps (and I don't see how I would just introduce i anyway).
 
Physics news on Phys.org
Factor out the 1/n^2. Can you write an expression for the sum (1+2+...+n)?
 
I'm not really sure what you mean.
 
Sean1218 said:
I'm not really sure what you mean.

I meant pretty much what I said. an=(1/n^2)*(1+2+...+n), right? Perhaps you know a formula for (1+2+...+n) in terms of n? If not, and you know how to integrate you can also do it as a Riemann sum. Can you write down a Riemann sum for the function f(x)=x between 0 and 1?
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 34 ·
2
Replies
34
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
4
Views
2K