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18 April, 07:54

Find the sum of the following infinite geometric series, if it exists.

one-third plus one-ninth plus one-twenty-seventh + one-eighty-first plus and so on

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  1. 18 April, 07:57
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    The sum of an infiinte series exists when the ratio is in the interval (-1,1)

    Here the ratio is 1/3, then the sum exists.

    The formula for this sum is A / (1 - r); where A is the first term and r is the ratio

    Then, the sum is [1/3] / [1 - 1/3] = [1/3] / [2/3] = 1/2

    Answer: 1/2
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