Analysis WebNotes
arrow_back arrow_forward

Class Contents

Monotonic Sequences

Example:

Keeps peaking--longer and shallower each time.

Monotonic sequences are much nicer.

In fact, even more is true.

What's cool about this theorem: You don't need to know what the sequence converges to, to show that it does converge.

Proof.

Example:

Claim:

Proof.

Claim:

Proof.

We have now proved that xn is increasing and bounded. Thus, xn converges. But, what is the limit of our sequence xn?

Click here to find out.

Proof.