Determine whether the geometric series converges or diverges.
27 + 18 + 12 + 8 + . . .
it diverges i think
To determine whether a geometric series converges or diverges, we need to check the common ratio of the series.
In this case, we can observe the pattern in the series:
27, 18, 12, 8, ...
To find the common ratio, we divide any term by its preceding term. Let's choose the second and first terms: 18/27 = 2/3.
The common ratio (r) in this series is 2/3.
Now, to determine if the series converges or diverges, we need to check the absolute value of the common ratio is less than 1. If the absolute value is less than 1, the series converges; if the absolute value is greater than or equal to 1, the series diverges.
In this case, the absolute value of 2/3 is less than 1.
Therefore, the geometric series with a common ratio of 2/3 converges.