Math 2602  B1, B2                                                                      Homework  #2
                                        Due Thursday, August 26, 2004


1. Determine whether   a_n = o(b_n) ,   b_n = o(a_n) ,   or neither.

    (i)  a_n = 5n³ ,   b_n = (3/2)ⁿ                                                       (*)                                                                                
                                          





 

  (ii)     a_n = n^½ ,   b_n = n/ln(n)                                                    (*)

 






  (iii)   a_n = n! ,  b_n = 2ⁿ                                                             (*)      

 
 





 (iv)   a_n = log₂(n²) ,   b_n = (log₂(n))²

 
 





 (v)    a_n = (n³ - 1)/n ,   b_n = 4n²                                                 (*)






(*)  from an old exam