一道数学题：1/x-1+1/(x-1)(x-2)+1/(x-2)(x-3)+.+1/(x-99)(x-100)
网友回答
原式=1/(x-1)+[1/(x-2)-1/(x-1)]+[1/(x-3)-1/(x-2)]……+[1/(x-100)-1/(x-99)]
=1/(x-1)-1/(x-1)+1/(x-2)-1/(x-2)+……+1/(x-99)-1/(x-99)+1/(x-100)
=0+0+……+1/(x-100)
=1/(x-100)
======以下答案可供参考======
供参考答案1:
1/x-1+1/(x-1)(x-2)+1/(x-2)(x-3)+......+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-1+{-1/(x-1)+1/(x-100)}=后面自己会算了吧