Sequence converge to what?

  • Thread starter pivoxa15
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  • #1
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Homework Statement


What does the sequence Sn={0n} for n large converge to?


The Attempt at a Solution


I think it converges to 0 since each n is finite although arbitarily large.
 

Answers and Replies

  • #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.
 
  • #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.
 
  • #4
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It should be n*0. So I was right.
 
  • #5
HallsofIvy
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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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