下面这道题怎么算,1/1*5+1/5*9+1/9*13+1/13*17……+1/37*41

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下面这道题怎么算,1/1*5+1/5*9+1/9*13+1/13*17……+1/37*41
下面这道题怎么算,
1/1*5+1/5*9+1/9*13+1/13*17……+1/37*41

下面这道题怎么算,1/1*5+1/5*9+1/9*13+1/13*17……+1/37*41
1/(1*5)=1/4(1/1-1/5)
1/(5*9)=1/4(1/5-1/9)
依次类推再相加
得1/4(1/1-1/5+1/5-1/9+1/9.-1/37+1/37-1/41)
=1/4(1/1-1/41)
=10/41

每个分数都可以拆开
1/1*5=(1/4)*(1-1/5)
1/5*9=(1/4)*(1/5-1/9)
1/13*17=(1/4)*(1/13-1/17)
……
1/37*41 =(1/4)*(1/37-1/41)
原式==(1/4)*(1-1/5+1/5-1/9+1/9-1/13……+1/37-1/41)
【中间的项都消掉了】...

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每个分数都可以拆开
1/1*5=(1/4)*(1-1/5)
1/5*9=(1/4)*(1/5-1/9)
1/13*17=(1/4)*(1/13-1/17)
……
1/37*41 =(1/4)*(1/37-1/41)
原式==(1/4)*(1-1/5+1/5-1/9+1/9-1/13……+1/37-1/41)
【中间的项都消掉了】
==(1/4)*(1-1/41)
==10/41

收起

原式=1/4(1/1-1/5+1/5-1/9+1/9....-1/37+1/37-1/41)
=1/4(1/1-1/41)
=10/41

原式=1/4(1/1-1/5+1/5-1/9+1/9....-1/37+1/37-1/41)
=1/4(1/1-1/41)
=10/41