(-1/2)-(-1/3)-(+1/4)
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(-1/2)-(-1/3)-(+1/4)
(-1/2)-(-1/3)-(+1/4)
(-1/2)-(-1/3)-(+1/4)
(-1×1/2)+(-1/2×1/3)+(-1/3×1/4)+……+(-1/2004×1/2005)
=-1/(1×2)+[-1/(2×3)]+[-1/(3×4)]+……+[-1/(2004×2005)]
=-(1/1-1/2)+[-(1/2-1/3)]+[-(1/3-1/4)]+……+[-(1/2004-1/2005)]
=-1+1/2-1/2+1/3-1/3+1/4-……-1/2004+1/2005
=-1+1/2005
=-2004/2005
1()2()3()4
(-1/2)-(-1/3)-(+1/4)
(1-2/1)*(1-3/1)*(1-4/1)*.*(1-2007/1)*(1-2008/1)
200*(1-1/2)*(1-1/3)*(1-1/4)*.*(1-1/100)
(1+2/1)(1+4/1)(1+6/1).(1+10/)(1-3/1)(1—5/1).(1-9/1)
-1/2+(-1/6)-(-1/4)-2/3
1 2 3 4 ()
(1) (2) (3) (4) (5)
1)2)3)4)5)
1) 2) 3) 4) 5)
(-1×1/2)+(-1/2×1/3)+(-1/3×1/4)+…+(-1/2008×1/2009)
(-1*1/2)+(-1/2*1/3)+(-1/3*1/4).(-1/2012*1/2013)
(1*2)/1+(2*3)/1+(3*4)/1+.+2010*2011/1
(1-1/2)(1-1/3)(1-1/4).(1-1/100)
8+(-2)+(-4)+1+1+(-3)
(1,1,1).(2,4,8)...3Q
(-3/2)*(+1又1/3)*(-1-1/4) (-3/2)*(+1又1/3)*(-1-1/4)
计算:(1/50-1)(1/49-1)(1/48-1)…(1/4-1)(1/3-1)(1/2-1)