1/1x2+1/2x3+1/3x4+...+1/2007x2008=?

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1/1x2+1/2x3+1/3x4+...+1/2007x2008=?
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1/1x2+1/2x3+1/3x4+...+1/2007x2008=?
1/1x2+1/2x3+1/3x4+...+1/2007x2008=?

1/1x2+1/2x3+1/3x4+...+1/2007x2008=?
1/1x2+1/2x3+1/3x4+...+1/2007x2008
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2007-1/2008)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2007-1/2008
中间互相抵消
=1-1/2008
=2007/2008

1/1x2=1/1-1/2
1/2x3=1/2-1/3
.....
1/1x2+1/2x3+1/3x4+...+1/2007x2008
=1-1/2+1/2-1/3+.....+1/2007-1/2008
=1-1/2008
=2007/2008

原式=(1-1/2)+(1/2-1/3)…………+(1/2007+1/2008)
=1-1/2+1/2-1/3+1/3…………+1/2007-1/2008
=1-1/2008
=2007/2008

因为1/1×2=1-1/2
1/2×3=1/2-1/3
……
1/2007×2008=1/2007-1/2008
所以原式=1-1/2+1/2-1/3+1/3-1/4+……+1/2007-1/2008
=1-1/2008=2007/2008

是不是1*2、2*3……都是分母呀，否则真的不好做

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