简算(1/2+1/3+...+1/2003)(1+1/2+1/3+...+1/2004)-(1+1/2+1/3+...1/2003)(1/2+1/3+...+1/2004)
问题描述:
简算(1/2+1/3+...+1/2003)(1+1/2+1/3+...+1/2004)-(1+1/2+1/3+...1/2003)(1/2+1/3+...+1/2004)
答
设1/2+1/3+...+1/2003为n,1/2+1/3...+1/2004为m
有:n(1+m)-(1+n)m
=n+mn-m-mn
=n-m
=-1/2004