# Is this sequence divergent or convergent?

## 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?

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PeroK
Homework Helper
Gold Member

## 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?

If the limit does exist, what could it be?

If the limit does exist, what could it be?
Would the limit be 5 since sin(pi\2) is 1?

PeroK
Homework Helper
Gold Member
Would the limit be 5 since sin(pi\2) is 1?
How many different values does the sequence have?

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

PeroK
Homework Helper
Gold Member
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?

• Sarah Kenney
Ray Vickson
Homework Helper
Dearly Missed

## 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?

• 