1. ## Power Series

Show that there are integers {n sub j} where j goes from 1 to infinity is increasing to infinity such that lim j->infinity of x sub n sub j = p.

p is ro (not sure how it's spelled)

2. Originally Posted by jzellt
Show that there are integers {n sub j} where j goes from 1 to infinity is increasing to infinity such that lim j->infinity of x sub n sub j = p.

p is ro (not sure how it's spelled)
This is completely incomprehensible. Try LaTeX.

3. Originally Posted by jzellt
Show that there are integers {n sub j} where j goes from 1 to infinity is increasing to infinity such that lim j->infinity of x sub n sub j = p.

p is ro (not sure how it's spelled)
As far as I can tell this is asking us to show that there is a subsequence of the sequence $\{x_i ;\ i \in \mathbb{N}_+\}$ which converges to $\rho$. In which case there is missing information (the question is incomplete).

(there is also another problem, the subject line refers to series but the question to sequences)

CB

4. Sorry, I'm not familiar with LaTex. I've added an attachment...

I'm really at a loss with these. Any help is greatly appreciated..

Thanks

5. Originally Posted by jzellt
Sorry, I'm not familiar with LaTex. I've added an attachment...

I'm really at a loss with these. Any help is greatly appreciated..

Thanks
What are $\rho,\sigma$?

6. This is what's stated right before the problems: (Hope you can understand it)

Let {xn} be a bounded sequence of nonnegative real numbers. Define lim n->infinity sup xn = p to be the largest number p suth that each interval (p-e, p+e) (e = epsilon) contains xn, for infinitely many indices n. (The fact that such a p exists is a fundamental property of the real numbers.)