Question

计算1/x-1 1/(x-1)(x-2) 1/(x-2)(x-3)… 1/(x-99)(x-100)及规律是什么

Answer 1

原式=1/(X-1)-1/(X-2)+1/(X-2)-1/（X-3）+…+1/（X-99）-1/（X-100）

=1/(x-1） - 1/(x-100)

=(x-100)-(x-1)/(x-1)(x-100)

=-99/(x-1)(x-100)