Sequence converge to what?

1. Apr 12, 2007

pivoxa15

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. Apr 12, 2007

Gib Z

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. Apr 12, 2007

matt grime

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. Apr 12, 2007

pivoxa15

It should be n*0. So I was right.

5. Apr 13, 2007

HallsofIvy

Staff Emeritus
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.