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15 November, 20:51

give an example of a convergent infinite series whose sum equal 3/5. explain how you know your series converges and write out work to show that its sum is in fact 3/5

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  1. 15 November, 23:42
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    The series 1/5, 2/15, 4/45, 8/135 ... converges and sums up to 3/5

    Step-by-step explanation:

    Consider the infinite geometric series

    1/5, 2/15, 4/45, 8/135 ...

    With first term, a=1/5

    common ratio, r = ⅔

    The series converge because the common ratio, |r|<1.

    The sum to infinity of a geometric series, S = a / (1-r)

    S = 1/5 : (1-⅔) = 1/5 : 1/3 = 3/5

    Therefore, the geometric series 1/5, 2/15, 4/45, 8/135 ... sums up to 3/5.
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