Math H162 Brown 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.)