Is this sequence divergent or convergent?

[Sarah Kenney]

Homework Statement

I'm trying to find out whether or not this sequence diverges or converges. If it converges, then what's the limit.
{4+sin(1/2*pi*n)}

The Attempt at a Solution

This one is a bit confusing to me since sin oscillates between 1 and -1. So if you plug in (pi*infinity)/2, that would go back and forth. So does that mean that the limit does not exist?

Thanks in advance.

 

[PeroK]

Homework Statement

I'm trying to find out whether or not this sequence diverges or converges. If it converges, then what's the limit.
{4+sin(1/2*pi*n)}

The Attempt at a Solution

This one is a bit confusing to me since sin oscillates between 1 and -1. So if you plug in (pi*infinity)/2, that would go back and forth. So does that mean that the limit does not exist?

Thanks in advance.

If the limit does exist, what could it be?

 

[Sarah Kenney]

If the limit does exist, what could it be?

Would the limit be 5 since sin(pi\2) is 1?

 

[PeroK]

Would the limit be 5 since sin(pi\2) is 1?

How many different values does the sequence have?

 

[Sarah Kenney]

Oh, so because it oscillates between -1 and 1, then the limit is from 3 to 5?

 

[PeroK]

Oh, so because it oscillates between -1 and 1, then the limit is from 3 to 5?

You can only have one limit (at most)! The sequence takes only three values: 3, 4 and 5. Do you just have to work out what the limit is (if it exists), or do you have to prove it?

 

[Ray Vickson]

Homework Statement

I'm trying to find out whether or not this sequence diverges or converges. If it converges, then what's the limit.
{4+sin(1/2*pi*n)}

The Attempt at a Solution

This one is a bit confusing to me since sin oscillates between 1 and -1. So if you plug in (pi*infinity)/2, that would go back and forth. So does that mean that the limit does not exist?

Thanks in advance.

You need to review the basics: what is the definition of a limit? Does your sequence have the required properties?

 

[Sarah Kenney]

Ok, I think I've got it. It does not exist, since the sequence oscillates between 5, 4, and 3. Thanks!