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System of iterated equationsby daniel6874
Tags: linear algebra 
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#1
Sep2811, 09:31 PM

P: 64

The following came up in the context of a genetics question. With the convention that ae on the LHS have subscript _n+1 and on the RHS ae have subscript _n,
a = 2ad + bd b = 2ae + bd + be + 2cd + ce c = be + ce d = 2ad + 2ae + bd + be + ce e = bd + be + 2cd + ce If the initial values for the variables is a=b=d=e=1, c=0 does the ratio e/(a+b+c+d+e) converge as n gets large? Can the ratio be calculated without a computer? Mathematica gives that e/(a+b+c+d+e) is about 0.109 for n=20, FWIW. 


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