1/4-1/2+1/6-1/4+1/8-1/6+...+1/2008-1/2006计算题计算题1/4-1/2+1/6-1/4+1/8-1/6+...+1/2008-1/2006

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1/4-1/2+1/6-1/4+1/8-1/6+...+1/2008-1/2006计算题计算题1/4-1/2+1/6-1/4+1/8-1/6+...+1/2008-1/20061/4-1/2+1/6-

1/4-1/2+1/6-1/4+1/8-1/6+...+1/2008-1/2006计算题计算题1/4-1/2+1/6-1/4+1/8-1/6+...+1/2008-1/2006
1/4-1/2+1/6-1/4+1/8-1/6+...+1/2008-1/2006计算题
计算题1/4-1/2+1/6-1/4+1/8-1/6+...+1/2008-1/2006

1/4-1/2+1/6-1/4+1/8-1/6+...+1/2008-1/2006计算题计算题1/4-1/2+1/6-1/4+1/8-1/6+...+1/2008-1/2006
1/4-1/2+1/6-1/4+1/8-1/6+...+1/2008-1/2006
= -1/2 + (1/4 - 1/4) + (1/6 - 1/6) +...+ (1/2006 - 1/2006) + 1/2008
= 1/2008 - 1/2
= -1003/2008

1/4-1/2+1/6-1/4+1/8-1/6+...+1/2008-1/2006
=1/2008-1/2
=-1003/2008

原式=-1/2+1/2008(整理可得)
再通分,得结果为-1003/2008