Question

Find the sum, if it exists, of the infinite geometric series that is related to the infinite geometric sequence 1, 521; 1, 369; 1, 232;…. Round the value of r to the nearest hundredth, if needed.

a. 250.00
b. 200.00
c. 175.00
d. 150.00

Answer 1

To find the sum of an infinite geometric series, use the formula Sum = a / (1 - r), where 'a' is the first term and 'r' is the common ratio. For this series, the sum does not exist because the absolute value of the common ratio is greater than 1.

Step-by-step explanation:

To find the sum of an infinite geometric series, we use the formula:

Sum = a / (1 - r)

Where 'a' is the first term of the series and 'r' is the common ratio. In this case, the first term 'a' is 1 and the common ratio 'r' can be found by dividing the second term by the first term: 521 / 369 ≈ 1.41. Plugging these values into the formula gives:

Sum = 1 / (1 - 1.41)

To determine if the sum exists, we need to check if the absolute value of 'r' is less than 1. Since 1.41 is greater than 1, the sum for this series does not exist.