作业帮分式的化简：1/a-1 + 1/(a-1)(a-2) + 1/(a-2)(a-3) +.+ 1/(a-99)(a-100
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/10/05 10:04:50
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!
清晰点,
一般的我是明白的!
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)+1/(a-3)/1/(a-2)+……+1/(a-100)-1/(a-99)
=1/(a-100)
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)+1/(a-3)/1/(a-2)+……+1/(a-100)-1/(a-99)
=1/(a-100)
分式的化简：1/a-1 + 1/(a-1)(a-2) + 1/(a-2)(a-3) +.+ 1/(a-99)(a-100
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