1. Given a sequence {a_{n}}, does it converge or diverge?
Is this sequence increasing? decreasing? bounded above? bounded below?

Does the series ∑a_{n} converge or diverge? Does ∑(-1)^{n} a_{n} converge
or diverge? Is the sequence of partial sums {s_{n}} bounded above for this
series?

2. For the following number series (a) (b) (c) (d) (several different
series), determine whether they converge or diverge. If converges,
is convergence absolute or conditional?

May include hints and/or additional questions, such as:

- use comparison test to determine convergence/divergence;

- apply ratio test. What does it give? (convergence/divergence/inconclusive)

- can alternating series test be used for this series?

3. Given a power series, find its radius of convergence and interval of
convergence. (For the interval of convergence, don't forget to check
endpoints.)

Does the series converge at a specified point (eg x=1, x=-10)?

4. Find the sum of the series (some variation on geometric series,
typically). Represent a given function as a power series (use geometric
series and algebra; see 8.6).

Determine where this series converges.

5. (possibly) A true-false question that requires understanding of concepts but few computations.