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8 July, 07:18

Find the sum of the infinite series 1/3+4/9+16/27+64/81 + ... if it exists.

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  1. 8 July, 07:54
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    9/27, 12/27, 16/27

    So this is a geometric sequence as each term is 4/3 the previous term.

    Since the common ration is greater than one the sum of the series diverges, it does not exist. (The sum just keeps getting larger and larger)

    For a geometric series to have a sum r^2<1

    So that the normal sum ...

    s (n) = a (1-r^n) / (1-r) becomes if r^2<1

    s=a / (1-r)
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