2\1+6\5+12\11+20\19+30\29...+9900\9899

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2\1+6\5+12\11+20\19+30\29...+9900\9899
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2\1+6\5+12\11+20\19+30\29...+9900\9899
2\1+6\5+12\11+20\19+30\29...+9900\9899

2\1+6\5+12\11+20\19+30\29...+9900\9899
...题目写的有点不习惯.
裂项相消
原式=99-[1/(1*2)+1/(2*3)+...+1/(99*100)]
=99-[(2-1)/(1*2)+(3-2)/(2*3)+...+(100-99)/(99*100)]
=99-[1/1-1/2+1/2-1/3+...+1/99-1/100]
=99-(1-0.01)=98.01