Sum of Geometric Series
What is geometric series?
A geometric series is a sequence of numbers in which ratio of each succeeding term to the preceding term remains the same. This ratio is called common ratio of the GP.
What is the formula for sum of geometric series?
The formula to find sum of a geometric series is given as, S = a × (rn – 1)/(r – 1), where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.
When can we use the formula for the sum of an infinite geometric series?
The formula for the sum of an infinite geometric series can be used when the absolute value of the common ratio ∣r∣ is less than 1. In this case, the sum is given by:
S = a/(1 – r)
What happens if the common ratio r is greater than or equal to 1?
If the absolute value of the common ratio ∣r∣ is greater than or equal to 1, the series diverges, meaning it grows without bound as the number of terms increases.
What are some applications of geometric series in real life?
Geometric series have various applications in fields such as finance (e.g., compound interest calculations), population growth models, computer algorithms, and physics (e.g., modeling radioactive decay).
How to Find the Sum of Geometric Series
A geometric series is a sequence of numbers where each term after the first term is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In a geometric series, if the absolute value of the common ratio (∣r∣) is less than 1, the series converges to a finite value. Otherwise, it diverges (grows without bound). Let’s know more about sum of Geometric Series formula, derivation and examples in detail below.
How to Find the Sum of Geometric Series
Contact Us