分式的化简：1/a-1 + 1/(a-1)(a-2) + 1/(a-2)(a-3) +.+ 1/(a-99)(a-100)
问题描述：
分式的化简：1/a-1 + 1/(a-1)(a-2) + 1/(a-2)(a-3) +.+ 1/(a-99)(a-100)
清晰点,
一般的我是明白的!
答
1=(a-1)-(a-2)所以1/(a-1)(a-2)=[(a-1)-(a-2)]/(a-1)(a-2)=(a-1)/(a-1)(a-2)-(a-2)/(a-1)(a-2)=1/(a-2)-1/(a-1)同理,1=(a-2)-(a-3),得到1/(a-2)(a-3)=1/(a-3)/1/(a-2)后面以此类推所以原式=1/(a-1)+1/(a-2)-1/(a-1)+...