Understanding the Sum of a Geometric Series | Formula, Explanation, and Assumptions

formula for sum of geometric series

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

S = a * (1 – r^n) / (1 – r)

where:
– S is the sum of the geometric series
– a is the first term of the series
– r is the common ratio between terms
– n is the number of terms in the series

To understand this formula, let’s break it down:

1

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

S = a * (1 – r^n) / (1 – r)

where:
– S is the sum of the geometric series
– a is the first term of the series
– r is the common ratio between terms
– n is the number of terms in the series

To understand this formula, let’s break it down:

1. The term (1 – r^n) represents the difference between 1 and the nth power of the common ratio. This is because in a geometric series, each term is obtained by multiplying the previous term by the common ratio. So, the sum of this term represents the difference between all the terms summed up and the last term.

2. The denominator (1 – r) represents the difference between 1 and the common ratio. It is used to make sure that the denominator is not zero, which would lead to division by zero.

3. Finally, multiplying the difference term (1 – r^n) with the first term (a) and dividing it by (1 – r) gives us the sum of all the terms in the geometric series.

It’s worth noting that the formula assumes that the absolute value of the common ratio (r) is less than 1. Otherwise, the sum of the geometric series may not converge to a finite value.

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