1/x(x+1)+1/(x+1)(x+2)+...+1/(x+999)(x+1000)=?1/x(x+1)+1/(x+1)(x+2)+...+1/(x+999)(x+1000)等于多少,"/"代表分之,第一个就是x(x+1)分之1,说的好了多加分,
问题描述：
1/x(x+1)+1/(x+1)(x+2)+...+1/(x+999)(x+1000)=?
1/x(x+1)+1/(x+1)(x+2)+...+1/(x+999)(x+1000)等于多少,"/"代表分之,第一个就是x(x+1)分之1,说的好了多加分,
答
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)
=999/x(x+1000)
答
1/x-1/(x+1)+...+1/(x+999)-1/(x+1000)
=1/x-1/(x+1000)
答
把每一项都拆开如：1/(X+1)(X+2)=就等于1/(X+1)-1/(X+2)～这么样就胜两头,中间全抵消,结果你知道了吧,这只是一中方法,手机打字太累,若你是高中没必要深解,记住方法就行!
答
1/x(x+1)=1/X-1/(X+1)
1/(x+1)(x+2)=1/(X+1)-1/(X+2)
...
1/(x+999)(x+1000)=1/(X+999)-1/(X+1000)
所以原式=1/X-1/(X+1)+1/(X+1)-1/(X+2)+...+1/(X+999)-1/(X+1000)
=1/X-1/(X+1000)=999/X(X+1000)