geometric series (Meaning)
Wordnet
geometric series (n)
a geometric progression written as a sum
Synonyms & Antonyms of geometric series
No Synonyms and anytonyms found
geometric series Sentence Examples
- In mathematics, a geometric series is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed, non-zero number.
- The sum of a finite geometric series can be calculated using the formula Sn = a * (1 - r^n) / (1 - r), where "a" is the first term, "r" is the common ratio, and "n" is the number of terms.
- An example of a geometric series is 2 + 6 + 18 + 54 + ..., where each term is three times the previous term.
- Geometric series find applications in various fields, including finance, physics, and computer science.
- Infinite geometric series converge to a finite value if the absolute value of the common ratio is less than one.
- The sum of an infinite geometric series can be found using the formula S = a / (1 - r), where "a" is the first term and "r" is the common ratio.
- Engineers use geometric series to analyze circuits with resistors or capacitors arranged in a geometric progression.
- Mathematicians study the convergence and divergence of geometric series to understand their behavior under different conditions.
- Calculating the sum of a geometric series is crucial for determining the total value of investments with compound interest.
- Understanding geometric series is fundamental in calculus, particularly in the study of infinite series and sequences.
FAQs About the word geometric series
a geometric progression written as a sum
No synonyms found.
No antonyms found.
In mathematics, a geometric series is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed, non-zero number.
The sum of a finite geometric series can be calculated using the formula Sn = a * (1 - r^n) / (1 - r), where "a" is the first term, "r" is the common ratio, and "n" is the number of terms.
An example of a geometric series is 2 + 6 + 18 + 54 + ..., where each term is three times the previous term.
Geometric series find applications in various fields, including finance, physics, and computer science.
