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Find the sum of the infinite series 1/3 + 4/9 + 16/27 + 64/81 etc. if it exists.
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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.
Posted by justaguide on September 19, 2013 at 6:07 PM (Answer #1)
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