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Sequence converge to what?

  1. Apr 12, 2007 #1
    1. The problem statement, all variables and given/known data
    What does the sequence Sn={0n} for n large converge to?

    3. The attempt at a solution
    I think it converges to 0 since each n is finite although arbitarily large.
  2. jcsd
  3. Apr 12, 2007 #2

    Gib Z

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    I don't understand, is every term in the series 0 times n? Because yes that is 0. Your attempt at the solution is right.
  4. Apr 12, 2007 #3

    matt grime

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    Please write out your questions properly. What you've written doesn't make any sense. Is 0n supposed to be 0*n, for n in N? It clashes with what you mean by using Sn, you see. It is not right to say each n is finite though arbitrarily large. Each n is not arbitrarily large, each n is just an integer, and doesn't vary at all. There is no need to invoke 'finiteness of n'. 0*n=0 for all n in N. That is just a simple fact, so S_n=0 for all n. Constant sequences obvisouly converge.
  5. Apr 12, 2007 #4
    It should be n*0. So I was right.
  6. Apr 13, 2007 #5


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    I dislike "arbitrarily large" numbers!

    What you are saying is that the sequence is "eventually" n*0= 0.

    Or: There exist an integer N such that if n> N then Sn= 0.

    Yes, such a sequence converges to 0.
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