计算1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3).+1/(x+2003)(x+2004)求全过程谁能告诉_数学解答

计算1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3).+1/(x+2003)(x+2004)
求全过程谁能告诉我1/x-1/(x+1)是什么意思?怎么表达,是不是两个分数线?

人气：233 ℃　时间：2019-08-19 13:21:07

解答

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3).+1/(x+2003)(x+2004)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3).+1/(x+2003)-1/(x+2004)
=1/x-1/(x+2004)
=2004/（x²+2004x)
1/x-1/(x+1) 是分式1/x与1/(x+1)的差.
=(x+1-x)/x(x+1)
=1/x(x+1）