1/21/3+1/31/4+1/41/5.+1/20081/2009怎么解?

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1/2*1/3+1/3*1/4+1/4*1/5.+1/2008*1/2009怎么解?
1/2*1/3+1/3*1/4+1/4*1/5.+1/2008*1/2009怎么解?

1/2*1/3+1/3*1/4+1/4*1/5.+1/2008*1/2009怎么解?
=1/2-1/3+1/3-1/4+……+1/2008-1/2009
=1/2-1/2009
=2007/4018

1/2*1/3=1/2-1/3
1/N*1/（N+1）=1/N-1/（N+1）

本题即为1/2-1/2009=2007/4018

简便算法：1/2*1/3=1/6=1/2-1/3
1/3*1/4=1/12=1/3-1/4
以此类推，则1/2008*1/2009=1/2008-1/2009
所以原式=1/2-1/3+1/3-1/4+1/4-1/5……+1/2008-1/2009
=1/2-1/2009
=2007/4018

(1+1/2+1/3+1/4+1/5)*(1/3+1/4+1)-(1+1/3+1/4)*(1/2+1/3+1/4+1/5) 1+2+3+4+1 (1+1/2+1/3+1/40)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4)(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3+1/4),不好意思,是下面这个! /1/3-1/2/+/1/4-1/3/+/1/5-1/4/+.+/1/10-1/9/ |1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2008-1/2007| |1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/10-1/9| 1/2 1/3 1/4是勾股数吗 1/3+1/2+1/4 1/2*1/3*1/4 1/2+1/3+1/4=? 1/2-3/1-4/1= 1 2 3 4 1 2 3 4 1 2 3 4 1,2,3,4, 1 2 3 4 1 2 3 4 1,2,3,4,