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Is this sequence divergent or convergent?

  1. Nov 7, 2015 #1
    1. The problem statement, all variables and given/known data
    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)}

    3. 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.
     
  2. jcsd
  3. Nov 7, 2015 #2

    PeroK

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    If the limit does exist, what could it be?
     
  4. Nov 7, 2015 #3
    Would the limit be 5 since sin(pi\2) is 1?
     
  5. Nov 7, 2015 #4

    PeroK

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    How many different values does the sequence have?
     
  6. Nov 7, 2015 #5
    Oh, so because it oscillates between -1 and 1, then the limit is from 3 to 5?
     
  7. Nov 7, 2015 #6

    PeroK

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    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?
     
  8. Nov 7, 2015 #7

    Ray Vickson

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    You need to review the basics: what is the definition of a limit? Does your sequence have the required properties?
     
  9. Nov 7, 2015 #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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