# Proof: Upper and lower limits

Not what you're looking for? Search our solutions OR ask your own Custom question.

Please see the attached file for the fully formatted problems.

Let be a sequence of real numbers.

We define

and

I'm having trouble with the following three proofs:

1) Show that

2) Show that if the limit of only exists when , then .

3) Show that if , then the limit exists, and .

https://brainmass.com/math/calculus-and-analysis/proof-upper-lower-limits-10178

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Let be a sequence of real numbers.

We define

and

I'm having trouble ...

#### Solution Summary

Proofs are provided for three statements involving limits. The solution is detailed and well presented.

$2.49