(1/2+1/3+...+1/2001)(1+1/2...+1/2000)-(1+1/2...+1/2001)(1/2+1/3+...+1/2001)

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(1/2+1/3+...+1/2001)(1+1/2...+1/2000)-(1+1/2...+1/2001)(1/2+1/3+...+1/2001)

(1/2+1/3+...+1/2001)(1+1/2...+1/2000)-(1+1/2...+1/2001)(1/2+1/3+...+1/2001)
(1/2+1/3+...+1/2001)(1+1/2...+1/2000)-(1+1/2...+1/2001)(1/2+1/3+...+1/2001)

(1/2+1/3+...+1/2001)(1+1/2...+1/2000)-(1+1/2...+1/2001)(1/2+1/3+...+1/2001)
=-1/2001 *(1/2+1/3+...+1/2001)