(1/2+1/3+...+1/2009)(1+1/2...+1/2008)-(1+1/2+...+1/2009)(1/2+1/3+...+1/2008)

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(1/2+1/3+...+1/2009)(1+1/2...+1/2008)-(1+1/2+...+1/2009)(1/2+1/3+...+1/2008)(1/2+1/3+...+1/2009)(1+1

(1/2+1/3+...+1/2009)(1+1/2...+1/2008)-(1+1/2+...+1/2009)(1/2+1/3+...+1/2008)
(1/2+1/3+...+1/2009)(1+1/2...+1/2008)-(1+1/2+...+1/2009)(1/2+1/3+...+1/2008)

(1/2+1/3+...+1/2009)(1+1/2...+1/2008)-(1+1/2+...+1/2009)(1/2+1/3+...+1/2008)
(1\2+1\3+...+1\2009)(1+1\2+...+1\2008) -(1+1\2+...+1\2009)(1\2+1\3+...+1\2008) =(1\2+1\3+...+1\2009)+(1\2+1\3+...+1\2009)(1\2+...+1\2008) -(1\2+1\3+...+1\2008)-(1\2+...+1\2009)(1\2+1\3+...+1\2008) =(1\2+1\3+...+1\2009) - (1\2+1\3+...+1\2008) = 1/2009