Find in some textbook the "Binomial Theorem" and prove it by mathematical induction. Then consider the sequence a_n defined by

Use the Binomial Theorem to determine whether a_n is monotone. Finally prove that a_n is bounded.

If you want to work on this extra credit internet special, which is worth 30 points (only if all parts of the problem are addressed), you have to turn it in no later than February 21, 2002, absolutely no later than 3:30 pm in either my office SH-311 or in my mailbox in the second floor of the Crawford building.