（1/2013-1）x(1/2012-1)x(1/2011-1)x……x(1/1000-1)
1个回答
(1/2013-1) x (1/2012-1) x (1/2011-1) x…x (1/1001-1) x (1/1000-1)
=
- (1-1/2013) x - (1-1/2012) x - (1-1/2011) x…x - (1-1/1001) x
-(1-1/1000)
//因为一共是2013-1000+1=1014个数字相乘,所以一共提取出来1014个负号,最后相乘得正
=
(1-1/2013) x (1-1/2012) x (1-1/2011) x…x (1-1/1001) x (1-1/1000)
=
(2012/2013) x (2011/2012) x (2010/2011) x…x (1000/1001) x
(999/1000)
= ( 2012 x 2011 x 2010 x...x 1000 x 999 ) / ( 2013 x 2012 x
2011 x...x 1001 x 1000 )
= 999/2013
亲,给个好评吧
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