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Math Help - Iternation definition

  1. #1
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    Iternation definition

    How do I work out an iterative definition (difference equation) for the sequences:
    (i). {1, 1/4, 1/9, 1/16...}
    (ii). {3, -6, 12, -24...}

    Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by tkexer View Post
    How do I work out an iterative definition (difference equation) for the sequences:
    (i). {1, 1/4, 1/9, 1/16...}
    (ii). {3, -6, 12, -24...}

    Thanks.
    i. The n-the term is 1/n^2 so:

    \frac{1}{(n+1)^2} = \frac{1}{(1+\frac{1}{\sqrt{1/n^2}})^2}

    so:

     <br />
a_{n+1}=\frac{1}{(1+\frac{1}{\sqrt{a_n}})^2},\ \ \ a_1=1<br />

    RonL
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