Question

How do you show that if limsn is defined then lim inf sn = lim sn = lim sup sn?

A. By demonstrating that the sequence is bounded.

B. By showing that the limit is unique and finite.

C. By proving that the infimum, limit, and supremum are all equal.

D. By using the Cauchy convergence criterion.

Answer 1

To show that if limsn is defined, then lim inf sn = lim sn = lim sup sn, we can use the fact that lim sn = lim sup sn = lim inf sn.

Step-by-step explanation:

To show that if limnsn is defined, then lim inf sn = lim sn = lim sup sn, we can use the fact that lim sn = lim sup sn = lim inf sn.
Here are the steps to prove this:
1. First, we need to show that the limit exists. If lim sn exists, then we have the equality lim sn = lim sup sn = lim inf sn.
2. Next, we need to show that the limit is unique. If the limit is unique, then we have the equality lim sn = lim sup sn = lim inf sn.
3. Finally, we need to show that the limit is finite. If the limit is finite, then we have the equality lim sn = lim sup sn = lim inf sn.