Criterion I：If the sequence , and satisfies the following conditions:

　　(1) ;

　　(2) , ,

Then the limit of the sequence exists, and .

　　Proof: Because , , according to the definition of sequence limit , for any given , there are positive integers , , such that when , there is always

,

When , there is always

.

Taking , then when , there are

, ,

According to the properties of absolute values , we have

, .

Therefore, when , there is always

,

Right now

,

So . Certification completed.

　　Note: The key to using the pinch criterion to find the limit is to construct and so that the limits of and are the same and easy to find.