Find the sum, if it exists, of the infinite geometric series, 3 plus 3 over 5 plus 3 over 25 plus 3 over 125 plus etc . (4 points)
I got c ( 15/4 ) is this right? Please check.
A) 1
B) 1 over 5
C) 15 over 4
D) Sum does not exist
correct
To find the sum of an infinite geometric series, you need to calculate the common ratio and determine whether it is within the range of -1 and 1. If it is within this range, the sum exists and can be calculated using the formula S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.
In this case, the first term (a) is 3. To find the common ratio (r), divide each term by the previous term. From the given series, we can see that:
3 / (3/5) = (3/5) / (3/25) = (3/25) / (3/125) = ...
Simplifying the expressions, we get:
5/1 = 5/3 = 5/15 = ...
This means that the common ratio (r) is 5/3.
Since the common ratio is greater than 1, the sum of the infinite geometric series does not exist. Therefore, the correct answer is:
D) Sum does not exist