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](/uploads/image/z/15048589-13-9.jpg?t=%E4%B8%8B%E9%9D%A2%E8%BF%99%E9%81%93%E9%A2%98%E6%80%8E%E4%B9%88%E7%AE%97%2C1%2F1%2A5%2B1%2F5%2A9%2B1%2F9%2A13%2B1%2F13%2A17%E2%80%A6%E2%80%A6%2B1%2F37%2A41)
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