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Is this sequence divergent or convergent?

  • #1

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.
 

Answers and Replies

  • #2
PeroK
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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?
 
  • #3
If the limit does exist, what could it be?
Would the limit be 5 since sin(pi\2) is 1?
 
  • #4
PeroK
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Would the limit be 5 since sin(pi\2) is 1?
How many different values does the sequence have?
 
  • #5
Oh, so because it oscillates between -1 and 1, then the limit is from 3 to 5?
 
  • #6
PeroK
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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?
 
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  • #7
Ray Vickson
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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?
 
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  • #8
Ok, I think I've got it. It does not exist, since the sequence oscillates between 5, 4, and 3. Thanks!
 

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