1. For any two numbers a and b, a*b means $a+b-\frac{2011}{2}$.
Calculate: $1*2*3*...*2010*2011$.
$1*2=1+2-\frac{2011}{2}$
$(1+2-\frac{2011}{2})*3=1+2+3-\frac{2(2011)}{2}$
$\therefore 1*2*3*...*2010*2011=1+2+3+...+2011-\frac{2011(2011-1)}{2}$
$\frac{2011(2011+1)}{2}-\frac{2011(2011-1)}{2}$
$(2011\times 1006)-(2011\times 1005)$
$2011(1006-1005)=2011$
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