1/(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)+1/(x-3)(x-4)+...+1/(x-99)(x-100)
=1/(x-1)+1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+.+1/(x-100)-1/(x-99)
=1/(x-100)请问怎么得到第一步?1/(x-1)(x-2)
=[(x-1)-(x-2)]/(x-1)(x-2)
=(x-1)/(x-1)(x-2)-(x-2)/(x-1)(x-2)
=1/(x-2)-1/(x-1)
后面的同理可得