How to judge that the sequence does not converge and how to judge that the sequence does not converge to a?

If two subsequences converge to different values, the series diverges.

For example, an = (- 1) n

The sub-column composed of odd terms converges to-1, and the sub-column composed of even terms converges to 1, so {an} diverges.

Something about Cauchy should be like this:

There is an e0>0 for all n, n, m >；; N, so | an-am | >；; =e0 .

Then {an} diverges.

This is Cauchy's negative form.

There is also a negative form of definition expressed in this way.

There is an e0>0, and for all n, there is n0 >；; N, so | an0-a | >；; =e0 .

Then {an} diverges.

Tips for learning mathematics

1, you should be good at thinking when learning mathematics, and the answers you come up with are far more impressive than those others say.

2. Do a good preview before class, so that we can better digest and absorb the unknown knowledge points in math class.

3, the mathematical formula must be memorized, and it must be deduced and can be deduced.

4. The most basic thing to learn mathematics well is to master the knowledge points of textbooks and exercises after class.

5. 80% of the scores in mathematics come from the basic knowledge, and 20% of the scores are difficult, so it is not difficult to test 120.