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# Class Contents

## Monotonic Sequences

**What's cool about this theorem:** You don't need to know what the sequence converges to, to show that it does converge.**Claim:**
_{n} is increasing and bounded. Thus, x_{n} converges. But, what is the limit of our sequence x_{n}?

Example:

Keeps peaking--longer and shallower each time.

Monotonic sequences are **much** nicer.

In fact, even more is true.

Proof.

Example:

**Claim:**

We have now proved that x