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Simplify $$\sum_{n=a+1}^{2a}A_n- \sum_{n=2}^{a}A_n = \sum_{n=b+1}^{2b}A_n - \sum_{n=2}^{b}A_n$$ where $A$ is an infinite set of non-unique natural numbers

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What do you mean by simplify? You have an equation. It holds for $a=b$, though we can't say much more unless we know what $A_n$ is ... –  Calvin Lin Jan 28 '13 at 5:30
    
I assume you mean "each $A_n$ is an infinite set...? If yes, is there any relationship between the $A_n$s, such as $A_n \subset A_{n+1}$? –  gnometorule Jan 28 '13 at 5:54

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