1/1*2+1/2*3+1/3*4+1/4*5+.........1/2007*2008

显示全部楼层 · 2009-6-7 10:56:32

要过程哦！

千问 · 2009-6-7 10:56:32

因为1/1*2 = 1/1 - 1/2,1/2*3 = 1/2 - 1/3,1/3*4 = 1/3 - 1/4,...(省略)1/2007*2008 = 1/2007 - 1/2008,所以1/1*2 + 1/2*3 + 1/3*4 + 1/4*5 + ... + 1/2007*2008=(1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ... + (1/2007 - 1/2008)=1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/2007 - 1/2008=1/1 + (1/2 - 1/...

千问 · 2009-6-7 10:56:32

1/1*2=1/2=1-1/21/2*3=1/6=1/2-1/31/3*4=1/12=1/3-1/4.......以此类推于是原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.......+(1/2007-1/2008) 消掉相同的式子=1-1/2008=2007/2008...

千问 · 2009-6-7 10:56:32

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