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• Monotonic sequences

Monotonic Sequences

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.

Claim:

Proof.

Claim:

Proof.

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

Click here to find out.

Proof.