What is convergence and divergence?

There is a limit (the limit is not infinite) that means convergence, and there is no limit (the limit is infinite) that means divergence.

For example: f(x)= 1/x When x tends to infinity, the limit is 0, so it converges.

F(x)= x When x tends to infinity, the limit is infinite, that is, there is no limit, so it diverges.

In mathematical analysis, the concept opposite to convergence is divergence.

Extended data:

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. One of the counterexamples is harmonic series.

Medieval mathematician oris proved the divergence of harmonic series.

Universal series u 1+u2+...+un+ ...

Its terms are arbitrary series.

If the positive sequence σ ∣ un ∣ formed by the absolute value of the sequence σ u converges

Then σ un series is said to be absolutely convergent.

Convergence in economics is divided into absolute convergence and conditional convergence.

Conditional convergence means that, given the same technology and other conditions, countries with low per capita output have higher per capita output growth rate than countries with high per capita output, and a country's economy grows faster when it is far from equilibrium than when it is close to equilibrium.

Universal series u 1+u2+...+un+ ... All its terms are arbitrary series. If the positive sequence σ ∣ un ∣ composed of the absolute value of σ u converges, it is said that σ un is absolutely convergent.

If the series σ un converges and σ ∣ un ∣ diverges, it is said that the series σ un is conditionally convergent.