S R 1 I N-1 I-R Calculator

This calculator helps you compute the sum of a geometric series using the formula S = r(1 - i^n)/(1 - i). The result is displayed in a clear format with optional visualization.

What is S r 1 i n-1 i-r?

The S r 1 i n-1 i-r formula represents the sum of a geometric series where:

S is the sum of the series
r is the first term of the series
i is the common ratio between terms
n is the number of terms

This formula is commonly used in mathematics, finance, and physics to calculate the cumulative value of a series with a constant ratio between terms.

How to calculate S r 1 i n-1 i-r

To calculate the sum of a geometric series using this formula:

Identify the first term (r)
Determine the common ratio (i)
Count the number of terms (n)
Apply the formula: S = r(1 - i^n)/(1 - i)

Use our calculator to perform these calculations quickly and accurately.

Formula

S = r(1 - i^n)/(1 - i)

Where:

S = Sum of the series
r = First term of the series
i = Common ratio between terms
n = Number of terms

Note: This formula is valid when the common ratio i is not equal to 1. If i = 1, the series is arithmetic and the sum is calculated differently.

Example calculation

Let's calculate the sum of a geometric series with:

First term (r) = 2
Common ratio (i) = 0.5
Number of terms (n) = 5

Using the formula:

S = 2(1 - 0.5^5)/(1 - 0.5) = 2(1 - 0.03125)/0.5 = 2(0.96875)/0.5 = 3.875

The sum of this geometric series is 3.875.

FAQ

What is the difference between arithmetic and geometric series?

An arithmetic series has a constant difference between terms, while a geometric series has a constant ratio between terms. The sum formulas for these series are different.

When is the geometric series formula valid?

The formula S = r(1 - i^n)/(1 - i) is valid when the common ratio i is not equal to 1. If i = 1, the series is arithmetic and requires a different calculation method.

Can I use this calculator for financial calculations?

Yes, this calculator can be used for financial calculations involving geometric series, such as calculating the present value of an annuity or the future value of a series of investments with a constant growth rate.