Answer: To find the sum of an alternating series, use the formula for the sum of an infinite alternating series: Sum = a / (1 – r), where “a” is the first term and “r” is the common ratio between consecutive terms.
The sum of an infinite alternating series can be found using a specific formula. If the alternating series is in the form:
a − ar + ar2 − ar3+…
where a is the first term and r is the common ratio between consecutive terms, the sum S of the series is given by the formula:
S =
This formula is derived from the concept of geometric series. It’s important to note that the formula is applicable only when the absolute value of the common ratio ∣r∣ is less than 1, ensuring that the series converges to a finite sum. If ∣r∣ is greater than or equal to 1, the series diverges, and the sum is undefined.