Final answer:
To find the sum of the infinite geometric series given, use the formula S = a/(1-r), where a is the first term and r is the common ratio.
Step-by-step explanation:
To find the sum of an infinite geometric series, we must first determine if the series is convergent or divergent. For a geometric series to be convergent, the common ratio (r) must be between -1 and 1, exclusive.
In this series, the common ratio is 54/81 = 2/3, which is less than 1 in absolute value. Therefore, the series converges.
The formula to find the sum of an infinite convergent geometric series is S = a/(1-r), where a is the first term and r is the common ratio.
So, for this series, S = 81/(1-(2/3)) = 81/(1/3) = 81*3 = 243.