A, the original divergence, such as1/2+1/3+1/4+1/5+,,;

B, after changing to staggered series,1/2-1/3+1/4-1/5+,

Because the general term tends to 0, the positive and negative are staggered, so it converges.

This is conditional convergence.

Generic term = generic $ TERM

Staggered series = alternating series.

2. Absolute convergence = absolute convergence

That is, a series that still converges after taking an absolute value, that is, after taking all positive values,

Is an absolutely convergent series.

For example:

1/ 1? - 1/2? + 1/3? - 1/4? +,,,,are absolutely convergent series; because

1/ 1? + 1/2? + 1/3? + 1/4? +,,,,is a convergent series, equal to π? /6;

So,11? - 1/2? + 1/3? - 1/4? +,,,Convergence is called absolute convergence.