Understanding the Formula for the Sum of Infinite and Finite Geometric Series

formula for sum of infinite geometric series

The formula for the sum of an infinite geometric series is given by:

S = a / (1 – r)

Where:
– S represents the sum of the infinite geometric series

The formula for the sum of an infinite geometric series is given by:

S = a / (1 – r)

Where:
– S represents the sum of the infinite geometric series.
– a refers to the first term of the series.
– r is the common ratio between consecutive terms of the series.

To use this formula, it is important to note that for the series to converge (i.e., have a finite sum), the absolute value of the common ratio (|r|) must be less than 1.

In other words, if |r| < 1, then the infinite geometric series converges and has a finite sum. However, if |r| ≥ 1, the series diverges, meaning it does not have a finite sum. If you want to find the sum of a finite geometric series with 'n' terms, you can still use the formula above by substituting the value of 'n' in place of infinity. The formula for the sum of a finite geometric series is: S = a * (1 - r^n) / (1 - r) Where 'S' is the sum, 'a' is the first term, 'r' is the common ratio, and 'n' represents the number of terms in the series. It's important to note that the formula for the sum of an infinite geometric series assumes that the series converges. If it diverges, meaning it does not have a finite sum, then the formula does not hold.

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