can you explain that in English？

Certainly! Here's the explanation in English:

The convergence or divergence of a geometric series depends on the absolute value of its common ratio.

1. When the absolute value of the common ratio is less than 1, i.e., |r| < 1, the series converges to a finite value. The sum can be calculated using the formula: S = a/(1-r), where 'a' represents the first term and 'r' represents the common ratio. For example, if a = 2 and r = 0.5, then the sum of the geometric series is S = 2/(1-0.5) = 4.

2. When the absolute value of the common ratio is greater than or equal to 1, i.e., |r| >= 1, the series diverges, meaning it does not have a finite sum. In this case, it is not possible to calculate the sum of the geometric series.

In summary, the convergence or divergence of a geometric series depends on the absolute value of its common ratio. When |r| < 1, the series converges; when |r| >= 1, the series diverges.