Final answer:
To find the sum of the given infinite geometric series, calculate the common ratio by dividing a term by the preceding term, then use the formula for the sum of an infinite geometric series, S = a / (1 - r), ensuring that -1 < r < 1.
Step-by-step explanation:
The question asks to find the sum of an infinite geometric series given the first few terms of its related sequence. Looking at the given terms {1,521; 1,369; 1,232;...}, we first need to determine the common ratio (r). This is done by dividing a term in the sequence by the term before it. For example, dividing the second term by the first term: 1,369 ÷ 1,521. Using a calculator, this gives a value for r that we round to the nearest hundredth if needed.
Once r is found, we can use the formula for the sum of an infinite geometric series which is S = a / (1 - r), where a is the first term in the sequence. Substituting the values into the formula will give the sum provided that |r| < 1, since the sum of an infinite geometric series only exists when the common ratio is between -1 and 1 (exclusive).