分式化简：（1）1/x-1/(X+1) (2)1/x(x+1)+1/(X+1)(x+2)+...+1/（x+999)(x+1000_数学解答

分式化简：（1）1/x-1/(X+1) (2)1/x(x+1)+1/(X+1)(x+2)+...+1/（x+999)(x+1000)

人气：386 ℃　时间：2020-02-05 17:09:25

解答

（1）1/x-1/(x+1)=（x+1-x）/（x（x+1））=1/(x(x+1))(2)1/x(x+1)+1/(X+1)(x+2)+...+1/（x+999)(x+1000)=1/x-1/(x+1）+1/(x+1)-1/(x+2)+……+1/(x+999)-1/(x+1000)=1/x-1/(x+1000)=(x+1000-x)/(x(x+1000))=1000/(x(x...