Convergence and Sum of the Geometric Series: A Quick Guide

Click For Summary

Homework Help Overview

The original poster presents a problem involving the calculation of a series, specifically the sum of a series from n=1 to infinity of 1/n, which is identified as a geometric series. Participants are discussing the nature of the series and its convergence properties.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants question whether the series is indeed a geometric series, prompting discussions about the definition and characteristics of geometric series. Others express uncertainty about how to approach the problem and seek guidance on starting points for solving it.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the series and its properties. Some have noted that the series does not converge, while others are attempting to clarify the original problem statement and its requirements.

Contextual Notes

There is confusion regarding the terminology used in the problem, particularly the use of "geometric" to describe the series. Participants are also reflecting on their understanding of similar series and the implications of convergence or divergence.

Jimmy84
Messages
190
Reaction score
0
Geometric series problem urgent

Homework Statement



Calculate the geometric series of Ʃfrom n=1 to infinity of 1/n

Homework Equations





The Attempt at a Solution


I don't know how to start solving, how can I solve this? I have test about this tomorrow I really need some help please.
 
Physics news on Phys.org


First off, what is a geometric series? Are you sure that your series is a geometric series?
 


Mark44 said:
First off, what is a geometric series? Are you sure that your series is a geometric series?

the formula is Ʃ from n=0 to ∞ of a(r)^n is equal to a/(1-r)

I was told to use the geoemtric series and to solve for that. but I don't know any general process or any way to do that. how can I start to solve that?
 


The general term of a geometric series looks like this: ark. Does your series look like this?

It would be helpful to see the exact wording of your problem. What you have makes almost no sense.
 


Mark44 said:
The general term of a geometric series looks like this: ark. Does your series look like this?

It would be helpful to see the exact wording of your problem. What you have makes almost no sense.

thats what I have there arent many details i solved some similar problems for instance

Ʃ from n = 0 to ∞ of 1/2^n by subsituing this in the a/(1-r) expression the result was 2

but on this problem I don't see how could I make such a substitution.
 


Jimmy84 said:

Homework Statement



Calculate the geometric series of Ʃfrom n=1 to infinity of 1/n

Homework Equations





The Attempt at a Solution


I don't know how to start solving, how can I solve this? I have test about this tomorrow I really need some help please.
Are you sure that the word 'geometric' is in the problem in your book , wherever you got it.

This is a well known series that doesn't converge.
 


SammyS said:
Are you sure that the word 'geometric' is in the problem in your book , wherever you got it.

This is a well known series that doesn't converge.

Yes it is there
 


Ʃfrom n=1 to infinity of 1/n..this is harmonic series where the n is to the power of 1..
i just learned this in my class
 


SammyS said:
...

This is a well known series that doesn't converge.
Writing out the first bunch of terms gives:

1 + 1/2

 + 1/3 + 1/4     This is greater than 1/2, because 1/3 > 1/4

 + 1/5 + 1/6 + 1/7 + 1/8    > 1/2, because each fraction is at least 1/8

 + 9 + 1/10 + 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16  > 1/2, because each fraction is at least 1/16

 + ...

If you go far enough, you can exceed any number you like.
 
  • #10


Moderator's note: Thread moved to Calculus & Beyond section.
 
  • #11


This is a famous series...you will drill this into your head.
 
  • #12


Actually what are you calculating...? The sum? the convergence/divergence? limt?
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 13 ·
Replies
13
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K