Find the sum of the infinite series 1/3 + 4/9 + 16/27 + 64/81 etc. if it exists.
The sum of the infinite series `1/3 + 4/9 + 16/27 +...` has to be determined.
Notice the terms of the series. `(4/9)/(1/3) = (16/27)/(4/9) = 4/3`
This is a geometric series with the first term being `1/3` and the common ratio `4/3` .
As the common ratio is `4/3` which is greater than 1, it is not possible to determine the sum of an infinite number of terms of the series.
The required sum cannot be determined.