(1-1/2)×(1-1/3)×(1-1/4)×...×(1-1/2005)简便运算
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![(1-1/2)×(1-1/3)×(1-1/4)×...×(1-1/2005)简便运算](/uploads/image/z/436114-10-4.jpg?t=%281-1%2F2%29%C3%97%281-1%2F3%29%C3%97%281-1%2F4%29%C3%97...%C3%97%281-1%2F2005%29%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97)
(1-1/2)×(1-1/3)×(1-1/4)×...×(1-1/2005)简便运算
(1-1/2)×(1-1/3)×(1-1/4)×...×(1-1/2005)简便运算
(1-1/2)×(1-1/3)×(1-1/4)×...×(1-1/2005)简便运算
(1-1/2)×(1-1/3)×(1-1/4)×...×(1-1/2005)
=1/2*2/3*3/4*……*2003/2004*2004/2005=1/2005
=1/2×2/3×3/4×……×2004/2005 前一个的分母,是后一个的分子,可约去
=1/2005