18. Does the infinite geometric series diverge or converge? Explain.
4 + 12 + 36 + 108 + … (1 point)
It converges; it does not have a sum.
It diverges; it has a sum.
It converges; it has a sum.
It diverges; it does not have a sum.
Aren't you adding larger and larger terms ?
So what happens ?
It diverges without a sum
To determine if the given infinite geometric series converges or diverges, we need to check if the common ratio (r) is between -1 and 1. The common ratio is found by dividing any term by its preceding term.
In this series, we can see that each term is 3 times the previous term. Hence, the common ratio (r) is 3.
Since the common ratio (r) is greater than 1 (which is not between -1 and 1), the given infinite geometric series diverges.
So, the correct answer is: It diverges; it does not have a sum.