What would happen to the sum of a geometric series if the ratio was 1?

it would be infinite

Thank you!!

If the ratio of a geometric series is 1, then the series becomes a special case called an arithmetic series.

In a geometric series, each term is obtained by multiplying the previous term by a constant ratio. When the ratio is 1, each term is equal to the previous term. Consequently, the series no longer increases or decreases exponentially, but rather follows a linear pattern.

In an arithmetic series, each term is obtained by adding a constant difference to the previous term. Since the ratio is 1, the difference between consecutive terms is constant. Therefore, the sum of an arithmetic series can be found using the formula:

S = (n/2) * (a + L)

where S is the sum of the series, n is the number of terms, a is the first term, and L is the last term.

In this scenario, since the ratio is 1, the first term and the last term are the same. This implies that a = L. Therefore, the sum of the series simplifies to:

S = n * a

So, if the ratio of a geometric series is 1, the sum of the series would be equal to the number of terms multiplied by the value of each term.