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What is the sum of the series (1/2), (1/4), (1/8)...

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richardwalter | eNotes Newbie

Posted November 16, 2013 at 5:51 AM via web

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What is the sum of the series (1/2), (1/4), (1/8)...

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted November 16, 2013 at 5:56 AM (Answer #1)

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The terms with which the given series starts is `(1/2), (1/4), (1/8)`

The first term of the series is `1/2` . The ratio between two consecutive terms is `(1/8)/(1/4) = (1/4)/(1/2) = 1/2` . As the ratio is the same, this is a geometric series with first term `1/2` and common ratio `1/2` . As the number of terms of which the sum has to be determined is not given, the sum of infinite terms of the series has been determined.

This is equal to `(1/2)/(1 - 1/2) = 1`

The sum of infinite terms of the series `(1/2), (1/4), (1/8)... ` is 1.

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