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.
Thoughts on solving the convergence domain of function term series
Because the convergence domain of function term series is actually composed of all convergence points, the judgment of the convergence of function term series corresponding to each convergence point.
In fact, it corresponds to the judgment of the convergence of constant series, so the calculation of the convergence domain of function series is generally based on the judgment of constant series, the ratio convergence method based on the absolute value of terms and the root value discrimination method.