Question

4+12+36+108+....
Does the infinite geometric series diverge or converge?

Answer 1

what does it mean to diverge or converge? do you know?

Answer 2

it just keeps getting bigger, right?

Answer 3

it keeps going up and up. it never ends, therefore it is divergent

Answer 4

My answers are
it diverges; it has a sum
It diverges;it does not have a sum

Answer 5

For geometric series, the "common ratio", r, is the number that is multiplied to each successive term, starting with the first term. For the series you listed, the common ratio is r = 4.

In order for an infinite geometric series to have a finite sum, the terms need to get smaller and smaller. Getting smaller means that the absolute value of the common ratio, r, is less than 1.

Since |4| = 4 > 1, this series does not have a finite sum. We would say that this series diverges; it does not have a sum.