The following came up in the context of a genetics question. With the convention that a-e on the LHS have subscript _n+1 and on the RHS a-e have subscript _n,(adsbygoogle = window.adsbygoogle || []).push({});

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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# System of iterated equations

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