1/2x1/3+1/3x1/4+1/4x1/5……+1/99x1/100=?

1/2x1/3+1/3x1/4+1/4x1/5……+1/99x1/100=?
1/2x1/3+1/3x1/4+1/4x1/5……+1/99x1/100=?

1/2x1/3+1/3x1/4+1/4x1/5……+1/99x1/100=?
1/2x1/3+1/3x1/4+1/4x1/5……+1/99x1/100
=1/2-1/3+1/3-1/4+1/4-1/5……+1/99-1/100
=1/2-1/100
=49/100

=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/99-1/100)
中间正负抵消
=1/2-1/100
=49/100

=1/2-1/100=49/100
给你说明意思 步骤自己写 你不是着急吗
1/2*1/3=1/2-1/3
1/3*1/4=1/3-1/4 后边都一样
最后得出1/2-1/3+1/3-1/4......+1/99-1/100