Posted by Anonymous on Thursday, January 3, 2013 at 10:20am.
rearrange the terms to see that the first 2n terms are
1+3+5+... - 2(1+2+3+...)
= n^2 - 2(n(n+1)/2)
= n^2 - n^2-n
= -n
so, the average is -n/2n = -1/2
or, rearrange to see that the first 2n terms are
(1-2)+(3-4)+...+(n-(n+1))
= -1 + -1 + ...
= -n
average is -n/2n = -1/2
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