问题描述: 求1/X(X+3)+1/(X+3)(X+6)+……+1/(X+2007)(X+2010) 1个回答 分类:数学 2014-11-02 问题解答: 我来补答 1/x(x+3)=1/3*3/x(x+3)=1/3*[(x+3)-x]/x(x+3)=1/3*[(x+3)/x(x+3)-x/x(x+3)]=1/3*[1/x-1/(x+3)]其他的同样这么化简原式=1/3*[1/x-1/(x+3)]+1/3*[1/(x+3)-1/(x+6)]+……+1/3[1/(x+2007)-1/(x+2010)]=1/3*[1/x-1/(x+3)+1/(x+3)-1/(x+6)+……+1/(x+2007)-1/(x+2010)]中间正负抵消=1/3*[1/x-1/(x+2010)]=670/[x(x+2010)] 展开全文阅读