How to Find Sum of Alternating Series?

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 = [Tex]\frac{a}{1 – r}[/Tex]​

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.