令a=1\2+1\3+•••+1\2007则原式=(a+1/2008)(1+a)-(1+a+1/2008)a=a(1+a)+1/2008(1+a)-a(1+a)-1/2008a=1/2008(1+a)-1/2008a=1/2008+1/2008a-1/2008a=1/2008能不能不设呢？写起来麻烦你写出来嘛。✨不能没悬赏可以了吧。=(1/2+1/3+……+1/2007+1/2008)*(1+1/2+1/3+……+1/2007)-(1+1/2+1/3+……+1/2007+1/2008)*(1/2+1/3+……+1/2007)=(1/2+1/3+……+1/2007)*(1+1/2+1/3+……+1/2007)+1/2008(1+1/2+1/3+……+1/2007)-(1/2+1/3+……+1/2007)*(1+1/2+1/3+……+1/2007)-1/2008*(1/2+1/3+……+1/2007)=1/2008(1+1/2+1/3+……+1/2007)-1/2008*(1+1/2+1/3+……+1/2007)=1/2008+1/2008*(1+1/2+1/3+……+1/2007)-1/2008*(1+1/2+1/3+……+1/2007)=1/2008采纳吧