Whether each of the following sequence of numbers converges , and if so, please indicate the value at which it converges.

　　(1) (2) (3) (4).

　　Solution ：(1) The sequence is

It is easy to see that when increases infinitely, also increases infinitely, so the sequence is divergent ;

　　(2) The sequence is

It is easy to see that when increases infinitely, is infinitely close to , so the sequence converges to ;
　　(3) The sequence is

It is easy to see that when increases infinitely, repeatedly takes the two numbers and endlessly without getting infinitely close to any certain constant：, so the sequence is divergent ;

　　(4) The sequence is

It is easy to see that when increases infinitely, is infinitely close to , so the sequence converges to .