Question

What is a geometric progression? What determines the

convergence of a geometric progression?

Short answer

The series which is obtained by multiplying the terms by a fixed number is geometric progression.

The convergence of the geometric progression depends upon the common ratio.

Step-by-step solution

Step 1. Given information

The series which is obtained by multiplying the terms by a fixed number; the series following is in geometric progression :-

$a,ar,a{r}^2,....$

Step 2. Convergence of GP

The convergence of the geometric progression depends upon the common ratio.

If the common ratio is less than one, then the series is convergent.

If the common ration is greater than one, then the series is divergent.