In an infinite geometric series, the series gradually and eventually diverges or converges, this means that there may not always be a determinable sum because the values will continue increasing and there will theoretically always be another value in the series; it’s never ending I.e infinite

 

Infinite vs Finite series:

In a Finite series, n will always have a determined or determinable value because it is converging. This value can be calculated using the formula . In an Infinite geometric series however, n is Infinite due to it’s converging or diverging nature and therefor cannot be determined using the same formula. Instead we use the formula as demonstrated below.

Converging:

12, 6, 3…

r=o.5

 

diverging:

2, 8, 32…

r=4

NO POSSIBLE SUM