1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=?
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1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=?
![1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=?](/uploads/image/z/16982367-15-7.jpg?t=1%C3%971%2F2%2B1%2F2%C3%971%2F3%2B1%2F3%C3%971%2F4%E2%80%A6%E2%80%A6%2B1%2F2005%C3%971%2F2006%3D%3F)
1×1/2=1/2=1-1/2
1/2×1/3=1/6=1/2-1/3
1/3×1/4=1/12=1/3-1/4
.
1/2005×1/2006=1/2005-1/2006
所以1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006
=1-1/2+1/2-1/3+1/3-1/4+.+1/2005-1/2006
=1-1/2006
=2005/2006
1/2×1/3=1/6=1/2-1/3
1/3×1/4=1/12=1/3-1/4
.
1/2005×1/2006=1/2005-1/2006
所以1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006
=1-1/2+1/2-1/3+1/3-1/4+.+1/2005-1/2006
=1-1/2006
=2005/2006
计算:(1/2006-1)(1/2005-1)(1/2004)… (1/3-1)(1/2-1).
巧算:1×(1-1/2)×(1-1/3)×……×(1-1/2005)×(1-1/2006)×(1-1/2007)×(1-
计算:(1/2+1/3+1/4+…+1//2006)(1+1/2+1/3+…+1/2005)-(1+1/2+1/3+1/
2008-2007+2006-2005+…+4-3+2-1=
计算:(1/2+1/3+……+1/2006)(1+1/2+1/3+……+1/2005)-
(1/3+1/4……+1/2006)(1/2+1/3……+1/2006)-(1/2+1/3+……+1/2006)(1/3
1-2+3-4……+2005-2006
1+2+3+…+2004+2005+2006= 1+3+5+…+2001+2003+2005+2007
1+1/2+1/3+1/4+……+1/2004+1/2005+1/2006+1/2007+1/2008+1/2009+1
1+2-3-4+5…+2005+2006-2007-2008
1+2+3+4+···+2005+2006)/(1-1/1004)*(1-1/1005)……(1-1/2005)*(1-
(2007-1)+(2006-2)+(2005-3)+……+(1005-1003)