(1-1/2)*(1-1/3)*(1-1/4)*……*(1-1/2013)*(1-1/2014)
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![(1-1/2)*(1-1/3)*(1-1/4)*……*(1-1/2013)*(1-1/2014)](/uploads/image/z/1664176-40-6.jpg?t=%281-1%2F2%29%2A%281-1%2F3%29%2A%281-1%2F4%29%2A%E2%80%A6%E2%80%A6%2A%281-1%2F2013%29%2A%281-1%2F2014%29)
(1-1/2)*(1-1/3)*(1-1/4)*……*(1-1/2013)*(1-1/2014)
(1-1/2)*(1-1/3)*(1-1/4)*……*(1-1/2013)*(1-1/2014)
(1-1/2)*(1-1/3)*(1-1/4)*……*(1-1/2013)*(1-1/2014)
解
(1-1/2)*(1-1/3)*(1-1/4)*……*(1-1/2013)*(1-1/2014)
=(1/2)(2/3)(3/4)(4/5)……(2012/2013)(2013/2014)
=1×(1/2014)
=1/2014