Module 1 : Real Numbers, Functions and Sequences
Lecture 2 : Convergent & Bounded Sequences [ Section 2.2 : Convergent Sequences ]
 
 
          

                                      ,
                                     i.e.,   ,
                                     i.e.,   ,                   
    which is not true for every even ,   . Hence,  is not true. Similarly, we can show that is not possible for any   .
Though both sequence and are divergent, they are divergent for different reasons.
2.2.3   Examples:
(i)











 Consider the sequence .  We show that   Since

     <   ,
  Given  > 0, we will have  <  , if  
  So, if we choose such that  , then ,  .                   
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