Math H162   Brown   Wi05

Homework 1,  due January 7,  2005

 

Textbook: p.437-8, 1a through j.  Explain your answers. (for troubling ones, apply the technique suggested in problem 3 on p. 438.)

 

Problem A. (a)  Suppose that  a > -1.  Show that  (1 + a)n  is greater than or equal to  1 + na.  (Hint: Imitate the calculation given in class that 2n is greater than or equal to  1 + n  by replacing  2  by  1 + a in that calculation.)

 

(b)  Prove that if  |r| < 1, then  the limit as n  approaches infinity of  rn is 0. (Hint:  Use the fact that  1/|r| > 1 so that you can write  1/|r| = 1 + a where  a  > 0.  Now use part (a).)

 

Textbook: p. 437-8, #2, 3, 6