2. Convergence is an economic and mathematical term and an important tool for studying functions. It means to converge to a point and approach a certain value. The types of convergence are convergence sequence, functional convergence, global convergence and local convergence.
If a series is convergent, the terms of this series will definitely tend to zero. Therefore, any series whose term does not tend to zero is divergent. However, convergence is a stronger requirement than this: not every series whose term tends to zero converges.
Extended data:
Limit existence criterion of sequence convergence;
The necessary and sufficient conditions for the sequence {Xn} to converge are: for any given positive integer ε, there is such a positive integer n, when m >; N, n> When n | exists | xn-XM.
The geometric meaning of this criterion shows that the necessary and sufficient condition for the sequence {Xn} to converge is that, for any given positive number ε, the distance between any two points is less than ε in all the points Xn with sufficiently large numbers on the number axis.
In the process of directly proving recursive sequence by monotone boundedness principle, in order to verify its boundedness and monotonicity, it is usually necessary to calculate several terms to observe the possible changing law, and then verify it.
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