(1/2+1/3+...+1/2004)(1+1/2+...+1/2003)-(1+1/2+..+1/2004)(1/2+1/3+..+1/2003)

问题描述:

(1/2+1/3+...+1/2004)(1+1/2+...+1/2003)-(1+1/2+..+1/2004)(1/2+1/3+..+1/2003)

设x=1/2+1/3+...+1/2004
y=1/2+...+1/2003
(1/2+1/3+...+1/2004)(1+1/2+...+1/2003)-(1+1/2+..+1/2004)(1/2+1/3+..+1/2003)
=x(1+y)-(1+x)y
=x+xy-y-xy
=x-y
=1/2004