数学智力乐园规律 1/1x2+1/2x3= 1/1x2+1/2x3+1/3x4= 1/1x2+1/2x3+1/3x4+1/4x5= 要规律

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数学智力乐园规律 1/1x2+1/2x3= 1/1x2+1/2x3+1/3x4= 1/1x2+1/2x3+1/3x4+1/4x5= 要规律

数学智力乐园规律 1/1x2+1/2x3= 1/1x2+1/2x3+1/3x4= 1/1x2+1/2x3+1/3x4+1/4x5= 要规律
数学智力乐园规律 1/1x2+1/2x3= 1/1x2+1/2x3+1/3x4= 1/1x2+1/2x3+1/3x4+1/4x5= 要规律

数学智力乐园规律 1/1x2+1/2x3= 1/1x2+1/2x3+1/3x4= 1/1x2+1/2x3+1/3x4+1/4x5= 要规律
1/1x2=1/1-1/2;
1/2x3=1/2-1/3;
1/3x4=1/3-1/4;
1/4x5=1/4-1/5;
……
所以:
1/1x2+1/2x3=1/1-1/2+1/2-1/3=1-1/3=2/3;
1/1x2+1/2x3+1/3x4=1/1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4;
1/1x2+1/2x3+1/3x4+1/4x5=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5=1-1/5=4/5;
……

1/1*2=1/1 - 1/2
1/2*3=1/2 - 1/3
这样吧中间的都能消去
1/1x2+1/2x3= 1 -1/3=2/3
1/1x2+1/2x3+1/3x4=3/4
1/1x2+1/2x3+1/3x4+1/4x5= 4/5

1/1x2+1/2x3+1/3x4+1/4x5+1/5x6

原式=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)=1-1/5=4/5