(1) Observe the changing trend of the first term of the sequence： and draw its scatter diagrama scatter plot of the first terms of the sequence using calculation software ( see the figure below ) . From the scatter plot, the sequence seems to converge to .

　　After further calculation, the data in the above table are obtained. From the observation of the table results, it can be preliminarily judged that the sequence converges to , that is,

.

[ Detailed explanation of the experiment ]

　　(2) Observe the changing trend of the sequence when .

　　Using calculation software, we get

　　It can be seen from the results in the above table that as increases, gets closer and closer to . From this, we can preliminarily judge that the sequence converges to . In fact, Example 3 of this section gives a positive answer to this judgment.

[ Detailed explanation of the experiment ]