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I think that the Riemann series theorem is applicable here but I need some help organizing my thoughts.

The problem is: Let x be any real number. Prove there exists a way to rearrange a conditionally convergent series such that the sum is x.

I know I need to make the first few terms from the positive until their sum is bigger than x and then take enough negative terms so the their first two sums are less than x.

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What more do you need? –  vonbrand Apr 27 '13 at 23:26
    
just to see the steps more clearly would be helpful –  cswinson Apr 27 '13 at 23:29
    
Just pick your favorite conditionally convergent series (it would be helpful if the positive/negative terms diminish slowly), and pick some random $x$. Then do the process you describe, and do it for some other $x$. The number of terms to take each round probably won't come out any way regular (not one and one, or 2 and 5, or so unless you specifically target the values that result this way). –  vonbrand Apr 27 '13 at 23:35

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