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Math Help - finding value of summation of infinite series

  1. #1
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    finding value of summation of infinite series

    summation from k=0 to infinity of (3^(k-1))/(4^(3k+1)).

    Using the seq( and sum( functions on my calculator I get 16/183, but how do I do this without using a calculator.

    I wrote out the first few terms but nothing seemed to cross out.

    Thanks.
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  2. #2
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    Quote Originally Posted by WartonMorton View Post
    summation from k=0 to infinity of (3^(k-1))/(4^(3k+1)).

    Using the seq( and sum( functions on my calculator I get 16/183, but how do I do this without using a calculator.

    I wrote out the first few terms but nothing seemed to cross out.

    Thanks.
    Note that the thing you're summing can be written as \frac{1}{12} \left(\frac{3}{4^3} \right)^k.
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