1*2/1+2*3/1+3*4/1+4*5/1+省略号+99*100/1=
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![1*2/1+2*3/1+3*4/1+4*5/1+省略号+99*100/1=](/uploads/image/z/69111-63-1.jpg?t=1%2A2%2F1%2B2%2A3%2F1%2B3%2A4%2F1%2B4%2A5%2F1%2B%E7%9C%81%E7%95%A5%E5%8F%B7%2B99%2A100%2F1%3D)
1*2/1+2*3/1+3*4/1+4*5/1+省略号+99*100/1=
1*2/1+2*3/1+3*4/1+4*5/1+省略号+99*100/1=
1*2/1+2*3/1+3*4/1+4*5/1+省略号+99*100/1=
抄反了吧
1/1*2+1/2*3+1/3*4+1/4*5+省略号+1/99*100=这样吧
裂项
1/1*2=1-1/2
1/2*3=1/2-1/3
...
1/99*100=1/99-1/100
原式=1-1/2+1/2-1/3+1/3+1/4+...+1/99-1/100
=每两项抵消
=1-1/100
=99/100
1*2,2*3,3*4,4*5应该是分母,分解成
(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/99-1/100)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5……+1/99-1/100
=1-1/100 (中间两两抵消)
=99/100