Math H162 Ð Brown Ð Wi04

Homework 3, due Wednesday, January 21, 2004

Be sure to try these all right away, so that if some are sticky you can let your mind work on them offstage during the week.

** **

Textbook**:** p.446-450, #1 (this is
a short proof), 2bce, 4, 6b, 7d.

Problem
A. Use equation (3) on page 465 to find the sum of the series from n = 1 to
infinity of the terms

1/[(4n - 1)(4n + 1)]

(Sorry,
haven't yet figured out how to do a cap Greek sigma on both Word and the Web.)

Textbook:
p.454, #2, 4, 9, 12, 18, 22

Textbook:
p. 460, #4, 5, 8, 9b

Textbook:
p. 464, #2, 4, 6

Problem
B. Determine the behavior of the
series of positive terms in which the
nth term is

__(n!)(n!)__

(2n)!

Textbook:
p. 465, #18, 20, 22 (For #20, if
you need it use the fact that as
n goes to

infinity
the limit of (1 + 1/n)^{n} is e.)