Limit of a Sequence: Wayne's Inquiry

[wayneckm]

Hello all, indeed this is always a question in my mind.

For a sequence, we can study the limit, let's say $$\lim_{n\rightarrow\infty} x_{n} = c$$ where $$c$$ can be $$\infty$$.

So whenever we talk about this kind of limit, we are generally interested in a sequence which would not attain $$c$$ at a finite value of $$n$$. In other words, the sequence in the form of $$x_{n} = c$$ where $$n \geq N$$ for some finite $$N$$ is of no interest because the limit is trivial?

Thanks.


Wayne

 

[Office_Shredder]

If it becomes constant, then it's a pretty boring sequence, but unless you have some reason to believe so you shouldn't assume that the sequence can't be of that form. Do you have a specific context from which this question is coming?