# Does this series converge. (1 Viewer)

### Users Who Are Viewing This Thread (Users: 0, Guests: 1)

#### rcmango

1. The problem statement, all variables and given/known data

Does the series infinity n(sin(1/n)) converge?
E
n=1

2. Relevant equations

n

and

sin(1/n)

3. The attempt at a solution

The equation sin(1/n) looks familiar, maybe i could use the squeeze theorem?

something like -1 <= sin(1/n) <= 1

i'm not sure where to go after this though, or if i'm even on the right track?
thankyou.

#### arildno

Homework Helper
Gold Member
Dearly Missed
First check:
Does the general term go to zero as n goes to infinity?

#### Gib Z

Homework Helper
Yes You could use the squeeze theorem and get -|x|< sin(1/x) < |x|, but that doesn't seem the help you much. Do what arildno said, maybe a few other convergence tests, try using Taylor Series? I'd say it does, but can't show you right now.

#### dextercioby

Homework Helper
Since this is not an alternating series, then only answering the question posed by Arildno is enough to solve the problem.

Daniel.

#### lkh1986

There is a general formula: as x approaches 0, (sin x)/x approaches 1. So you can apply this in your question. Let n=1/x, then you modify the equation, then you will get the answer that the series diverge, since the series does not have a sum.

Last edited:

#### rcmango

First check:
Does the general term go to zero as n goes to infinity?
yes. i would say as n goes to infinity, it approaches 0.
the reasoning is because starting with small numbers it gets larger around .01745...

don't know where to go from here.

thanks for all the feedback, i found it all useful.

#### d_leet

yes. i would say as n goes to infinity, it approaches 0.
the reasoning is because starting with small numbers it gets larger around .01745...

don't know where to go from here.

thanks for all the feedback, i found it all useful.
Numbers at a certain point don't really tell you much about the behavior at infinity. Take the limit of the terms as n goes to infinity, if it isn't 0 what can you say about the series?

#### rcmango

Numbers at a certain point don't really tell you much about the behavior at infinity. Take the limit of the terms as n goes to infinity, if it isn't 0 what can you say about the series?
that it diverges.

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving