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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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JHockey | eNoter

Posted September 19, 2013 at 5:54 PM via web

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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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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 19, 2013 at 6:07 PM (Answer #1)

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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.

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