What Does the Sequence {0^n} Converge To?

[pivoxa15]

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.

 

[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.

 

[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.

 

[pivoxa15]

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

 

[HallsofIvy]

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 S_n= 0.

Yes, such a sequence converges to 0.