how to evaluate geometric series
Understand the Problem
The question is asking how to evaluate geometric series, which involves finding the sum of a series where each term is multiplied by a constant ratio from the previous term. This usually requires knowledge of the formula for the sum of a geometric series and its convergence criteria.
Answer
Use a1 ((1 - rn)/(1 - r)) for finite series and a1 / (1 - r) for infinite series with |r| < 1.
The final answer is the sum of a finite geometric series can be evaluated using the formula a1 ((1 - rn)/(1 - r)) and the sum of an infinite geometric series can be evaluated using the formula a1 / (1 - r) if the absolute value of r is less than 1.
Answer for screen readers
The final answer is the sum of a finite geometric series can be evaluated using the formula a1 ((1 - rn)/(1 - r)) and the sum of an infinite geometric series can be evaluated using the formula a1 / (1 - r) if the absolute value of r is less than 1.
More Information
The formula for the sum of a finite geometric series includes the first term, the common ratio, and the number of terms. For infinite geometric series, convergence only occurs when the absolute value of the common ratio is less than one.
Tips
Common mistakes include using the infinite series formula when the common ratio is not between -1 and 1, and confusing the formulas for finite and infinite series.
Sources
- Geometric Series - Varsity Tutors - varsitytutors.com
- How to Calculate a Geometric Series - Study.com - study.com
- Geometric Series - Formula, Examples, Convergence - Cuemath - cuemath.com
