这题我不会,化简 1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10).

题目

这题我不会,化简 1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10).

答案

原式=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+9)=1/(x+10)=1/(x+1)-1/(x+10)=9/(x+1)(x+10).
裂项相消,中间项全消了,只剩第一项减去最后一项,完成化简