化简1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4则1/(x-1)x+1/x(x+1)+1/(x+1)(x+2)+..+1/(x+9)(x+10)=

题目

化简1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4则1/(x-1)x+1/x(x+1)+1/(x+1)(x+2)+..+1/(x+9)(x+10)=

答案

原式=1/（x-1）-1/x+1/x-1/(x-2)+1/(x-2)-,+1/(x+9)-1/(x+10) =1/(x-1)-1/(x+10) 分解开来后除了首尾两项之外全都消去了,可得结果