Final answer:
The sum of a geometric series with a finite number of terms can be calculated using the formula Sn = a1 * (1 - rn)/(1 - r), where Sn is the sum, a1 is the first term, r is the common ratio, and n is the number of terms.
Step-by-step explanation:
Calculating the Sum of a Geometric Series
The equation to calculate the sum of a geometric series for a finite number of terms is given by:
Sn = a1 * (1 - rn) / (1 - r),
where:
- Sn is the sum of the first n terms of the series,
- a1 is the first term of the series,
- r is the common ratio between terms, and
- n is the number of terms.
This formula is applicable only if the absolute value of the common ratio r is less than 1 (|r| < 1). For an infinite geometric series, the sum converges to a finite number if |r| < 1, and the formula simplifies to S = a1 / (1 - r).