Convergence and Sum of the Geometric Series: A Quick Guide

[Jimmy84]

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.

 

[Mark44]

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

 

[Jimmy84]

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?

 

[Mark44]

The general term of a geometric series looks like this: ar^k. 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.

 

[Jimmy84]

The general term of a geometric series looks like this: ar^k. 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.

 

[SammyS]

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.

 

[Jimmy84]

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

 

[dadidudada]

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]

...

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.

 

[Mark44]

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

 

[flyingpig]

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

 

[flyingpig]

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