(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+.+(-1/2007x1/2008)+(-1/2008X1
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(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+.+(-1/2007x1/2008)+(-1/2008X1/2009)怎么算?
![(-1x1/2)+(-1/2x1/3)+(-1/3x1/4)+.+(-1/2007x1/2008)+(-1/2008X1](/uploads/image/z/17514421-61-1.jpg?t=%28-1x1%2F2%29%2B%28-1%2F2x1%2F3%29%2B%28-1%2F3x1%2F4%29%2B.%2B%28-1%2F2007x1%2F2008%29%2B%28-1%2F2008X1)
首先把负号提出来,则有
1x1/2=1-1/2
1/2x1/3=1/2-1/3
1/3x1/4=1/3-1/4
.
1/2008X1/2009=1/2008-1/2009
将以上各式相加,得原式=-(1-1/2009)=-2008/2009
1x1/2=1-1/2
1/2x1/3=1/2-1/3
1/3x1/4=1/3-1/4
.
1/2008X1/2009=1/2008-1/2009
将以上各式相加,得原式=-(1-1/2009)=-2008/2009
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